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Título : Algebraic Geometry and Geometric Modeling Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Mohamed Elkadi ; Bernard Mourrain ; Ragni Piene Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Mathematics and Visualization, ISSN 1612-3786 Número de páginas: X, 252 p. 52 illus., 27 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-33275-6 Idioma : Inglés (eng) Palabras clave: Mathematics Computer science Algebraic geometry Mathematical models Applied mathematics Engineering Geometry Modeling and Industrial Math Applications in Science Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects Nota de contenido: Algebraic geometry and geometric modeling: insight and computation -- Implicitization using approximation complexes -- Piecewise approximate implicitization: experiments using industrial data -- Computing with parameterized varieties -- Implicitization and Distance Bounds -- Singularities and their deformations: how they change the shape and view of objects -- Overview of topological properties of real algebraic surfaces -- Illustrating the classification of real cubic surfaces -- Bézier patches on almost toric surfaces -- On parametric surfaces of low degree in P3(C) -- On the intersection with revolution and canal surfaces -- A sampling algorithm computing self-intersections of parametric surfaces -- Elimination in generically rigid 3D geometric constraint systems -- Minkowski decomposition of convex lattice polygons -- Reducing the number of variables of a polynomial En línea: http://dx.doi.org/10.1007/978-3-540-33275-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34957 Algebraic Geometry and Geometric Modeling [documento electrónico] / SpringerLink (Online service) ; Mohamed Elkadi ; Bernard Mourrain ; Ragni Piene . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - X, 252 p. 52 illus., 27 illus. in color : online resource. - (Mathematics and Visualization, ISSN 1612-3786) .
ISBN : 978-3-540-33275-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Computer science Algebraic geometry Mathematical models Applied mathematics Engineering Geometry Modeling and Industrial Math Applications in Science Appl.Mathematics/Computational Methods of Clasificación: 51 Matemáticas Resumen: Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects Nota de contenido: Algebraic geometry and geometric modeling: insight and computation -- Implicitization using approximation complexes -- Piecewise approximate implicitization: experiments using industrial data -- Computing with parameterized varieties -- Implicitization and Distance Bounds -- Singularities and their deformations: how they change the shape and view of objects -- Overview of topological properties of real algebraic surfaces -- Illustrating the classification of real cubic surfaces -- Bézier patches on almost toric surfaces -- On parametric surfaces of low degree in P3(C) -- On the intersection with revolution and canal surfaces -- A sampling algorithm computing self-intersections of parametric surfaces -- Elimination in generically rigid 3D geometric constraint systems -- Minkowski decomposition of convex lattice polygons -- Reducing the number of variables of a polynomial En línea: http://dx.doi.org/10.1007/978-3-540-33275-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34957 Ejemplares
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Título : Algebraic Geometry and Commutative Algebra Tipo de documento: documento electrónico Autores: Siegfried Bosch ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Universitext, ISSN 0172-5939 Número de páginas: X, 504 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-4829-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Geometry Rings and Algebras Clasificación: 51 Matemáticas Resumen: Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature Nota de contenido: Rings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms En línea: http://dx.doi.org/10.1007/978-1-4471-4829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32195 Algebraic Geometry and Commutative Algebra [documento electrónico] / Siegfried Bosch ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - X, 504 p : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4471-4829-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Commutative algebra rings Geometry Rings and Algebras Clasificación: 51 Matemáticas Resumen: Algebraic geometry is a fascinating branch of mathematics that combines methods from both algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry (algebraic number theory, for example). The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts whilst more advanced readers can use the book to broaden their view on the subject. A separate part studies the necessary prerequisites from commutative algebra. The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. Therefore the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature Nota de contenido: Rings and Modules -- The Theory of Noetherian Rings -- Integral Extensions -- Extension of Coefficients and Descent -- Homological Methods: Ext and Tor -- Affine Schemes and Basic Constructions -- Techniques of Global Schemes -- Etale and Smooth Morphisms -- Projective Schemes and Proper Morphisms En línea: http://dx.doi.org/10.1007/978-1-4471-4829-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32195 Ejemplares
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Título : The Local Structure of Algebraic K-Theory Tipo de documento: documento electrónico Autores: Bjørn Ian Dundas ; SpringerLink (Online service) ; Thomas G. Goodwillie ; Randy McCarthy Editorial: London : Springer London Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Algebra and Applications, ISSN 1572-5553 num. 18 Número de páginas: XVI, 436 p Il.: online resource ISBN/ISSN/DL: 978-1-4471-4393-2 Idioma : Inglés (eng) Palabras clave: Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology K-Theory Topology Theory, Algebra Clasificación: 51 Matemáticas Resumen: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology Nota de contenido: Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K ? THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC En línea: http://dx.doi.org/10.1007/978-1-4471-4393-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32729 The Local Structure of Algebraic K-Theory [documento electrónico] / Bjørn Ian Dundas ; SpringerLink (Online service) ; Thomas G. Goodwillie ; Randy McCarthy . - London : Springer London : Imprint: Springer, 2012 . - XVI, 436 p : online resource. - (Algebra and Applications, ISSN 1572-5553; 18) .
ISBN : 978-1-4471-4393-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Category theory (Mathematics) Homological algebra K-theory Algebraic topology K-Theory Topology Theory, Algebra Clasificación: 51 Matemáticas Resumen: Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology Nota de contenido: Algebraic K-theory -- Gamma-spaces and S-algebras -- Reductions -- Topological Hochschild Homology -- The Trace K ? THH -- Topological Cyclic Homology -- The Comparison of K-theory and TC En línea: http://dx.doi.org/10.1007/978-1-4471-4393-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32729 Ejemplares
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Título : Algebraic Cobordism Tipo de documento: documento electrónico Autores: Marc Levine ; SpringerLink (Online service) ; Fabien Morel Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2007 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XII, 246 p Il.: online resource ISBN/ISSN/DL: 978-3-540-36824-3 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Commutative algebra rings K-theory Topology topology Geometry Rings and Algebras K-Theory Clasificación: 51 Matemáticas Resumen: Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications Nota de contenido: Introduction -- I. Cobordism and oriented cohomology -- 1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism. - II. The definition of algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism -- III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism and K-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5. Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented theories -- VI. Functoriality. 6.1. Refined cobordism. 6.2. Intersection with a pseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back and refined intersections. VII. The universality of algebraic cobordism. 7.1. Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3. Universality 7.4. Some applications -- Appendix A: Resolution of singularities -- References -- Index -- Glossary of Notation En línea: http://dx.doi.org/10.1007/3-540-36824-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34628 Algebraic Cobordism [documento electrónico] / Marc Levine ; SpringerLink (Online service) ; Fabien Morel . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2007 . - XII, 246 p : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-3-540-36824-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Commutative algebra rings K-theory Topology topology Geometry Rings and Algebras K-Theory Clasificación: 51 Matemáticas Resumen: Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications Nota de contenido: Introduction -- I. Cobordism and oriented cohomology -- 1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism. - II. The definition of algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism -- III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism and K-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5. Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented theories -- VI. Functoriality. 6.1. Refined cobordism. 6.2. Intersection with a pseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back and refined intersections. VII. The universality of algebraic cobordism. 7.1. Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3. Universality 7.4. Some applications -- Appendix A: Resolution of singularities -- References -- Index -- Glossary of Notation En línea: http://dx.doi.org/10.1007/3-540-36824-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34628 Ejemplares
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Título : Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Piotr Pragacz Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Trends in Mathematics Número de páginas: VIII, 236 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8537-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry topology Geometry Topology Clasificación: 51 Matemáticas Resumen: The articles in this volume are devoted to: - moduli of coherent sheaves; - principal bundles and sheaves and their moduli; - new insights into Geometric Invariant Theory; - stacks of shtukas and their compactifications; - algebraic cycles vs. commutative algebra; - Thom polynomials of singularities; - zero schemes of sections of vector bundles. The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber Nota de contenido: Notes on the Life and Work of Józef Maria Hoene-Wro?ski -- Exotic Fine Moduli Spaces of Coherent Sheaves -- Moduli Spaces of Coherent Sheaves on Multiples Curves -- Lectures on Principal Bundles over Projective Varieties -- Lectures on Torsion-free Sheaves and Their Moduli -- Miscellany on the Zero Schemes of Sections of Vector Bundles -- Thom Polynomials of Invariant Cones, Schur Functions and Positivity -- Geometric Invariant Theory Relative to a Base Curve -- Some Applications of Algebraic Cycles to Affine Algebraic Geometry -- to the Stacks of Shtukas En línea: http://dx.doi.org/10.1007/978-3-7643-8537-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34393 Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes [documento electrónico] / SpringerLink (Online service) ; Piotr Pragacz . - Basel : Birkhäuser Basel, 2008 . - VIII, 236 p : online resource. - (Trends in Mathematics) .
ISBN : 978-3-7643-8537-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry topology Geometry Topology Clasificación: 51 Matemáticas Resumen: The articles in this volume are devoted to: - moduli of coherent sheaves; - principal bundles and sheaves and their moduli; - new insights into Geometric Invariant Theory; - stacks of shtukas and their compactifications; - algebraic cycles vs. commutative algebra; - Thom polynomials of singularities; - zero schemes of sections of vector bundles. The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber Nota de contenido: Notes on the Life and Work of Józef Maria Hoene-Wro?ski -- Exotic Fine Moduli Spaces of Coherent Sheaves -- Moduli Spaces of Coherent Sheaves on Multiples Curves -- Lectures on Principal Bundles over Projective Varieties -- Lectures on Torsion-free Sheaves and Their Moduli -- Miscellany on the Zero Schemes of Sections of Vector Bundles -- Thom Polynomials of Invariant Cones, Schur Functions and Positivity -- Geometric Invariant Theory Relative to a Base Curve -- Some Applications of Algebraic Cycles to Affine Algebraic Geometry -- to the Stacks of Shtukas En línea: http://dx.doi.org/10.1007/978-3-7643-8537-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34393 Ejemplares
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