Algebraic Geometry over the Complex Numbers / Donu Arapura (2012)  

Público ISBD Título : Algebraic Geometry over the Complex Numbers Tipo de documento: documento electrónico Autores: Donu Arapura ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2012 Colección: Universitext, ISSN 0172-5939 Número de páginas: XII, 329 p. 17 illus., 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4614-1809-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebraic  geometry  Functions  of  complex  variables  Topology  Geometry  Several  Complex  Variables  and  Analytic  Spaces Clasificación: 51 Matemáticas Resumen: This textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. “Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory Nota de contenido: Preface -- 1. Plane Curves -- 2. Manifolds and Varieties via Sheaves -- 3. More Sheaf Theory -- 4. Sheaf Cohomology -- 5. de Rham Cohomoloy of Manifolds -- 6. Riemann Surfaces -- 7. Simplicial Methods -- 8. The Hodge Theorem for Riemann Manifolds -- 9. Toward Hodge Theory for Complex Manifolds -- 10. Kahler Manifolds -- 11. A Little Algebraic Surface Theory -- 12. Hodge Structures and Homological Methods -- 13. Topology of Families -- 14. The Hard Lefschez Theorem -- 15. Coherent Sheaves -- 16. Computation of Coherent Sheaves -- 17. Computation of some Hodge numbers -- 18. Deformation Invariance of Hodge Numbers -- 19. Analogies and Conjectures.- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-1809-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32773 Algebraic Geometry over the Complex Numbers [documento electrónico] / Donu Arapura ; SpringerLink (Online service) . - Boston, MA : Springer US, 2012 . - XII, 329 p. 17 illus., 1 illus. in color : online resource. - (Universitext, ISSN 0172-5939) . ISBN : 978-1-4614-1809-2 Idioma : Inglés (eng) Palabras clave: Mathematics  Algebraic  geometry  Functions  of  complex  variables  Topology  Geometry  Several  Complex  Variables  and  Analytic  Spaces Clasificación: 51 Matemáticas Resumen: This textbook is a strong addition to existing introductory literature on algebraic geometry. The author’s treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. “Algebraic Geometry over the Complex Numbers” is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory Nota de contenido: Preface -- 1. Plane Curves -- 2. Manifolds and Varieties via Sheaves -- 3. More Sheaf Theory -- 4. Sheaf Cohomology -- 5. de Rham Cohomoloy of Manifolds -- 6. Riemann Surfaces -- 7. Simplicial Methods -- 8. The Hodge Theorem for Riemann Manifolds -- 9. Toward Hodge Theory for Complex Manifolds -- 10. Kahler Manifolds -- 11. A Little Algebraic Surface Theory -- 12. Hodge Structures and Homological Methods -- 13. Topology of Families -- 14. The Hard Lefschez Theorem -- 15. Coherent Sheaves -- 16. Computation of Coherent Sheaves -- 17. Computation of some Hodge numbers -- 18. Deformation Invariance of Hodge Numbers -- 19. Analogies and Conjectures.- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-1809-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32773

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