Deformation Theory [recurso electrónico] / by Robin Hartshorne.
Tipo de material: TextoSeries Graduate Texts in Mathematics ; 257Editor: New York, NY : Springer New York, 2010Edición: 1Descripción: VIII, 236p. 19 illus. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9781441915962Tema(s): Mathematics | Geometry, algebraic | Mathematics | Algebraic GeometryFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 516.35 Clasificación LoC:QA564-609Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA564 -609 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 371386-2001 |
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QA564 -609 Symmetry and Spaces | QA564 -609 Cohomological and Geometric Approaches to Rationality Problems | QA564 -609 Nonlinear Computational Geometry | QA564 -609 Deformation Theory | QA564 -609 Generalizations of Thomae's Formula for Zn Curves | QA564 -609 Discrete Integrable Systems | QA564 -609 Liaison, Schottky Problem and Invariant Theory |
First-Order Deformations -- Higher-Order Deformations -- Formal Moduli -- Global Questions.
The basic problem of deformation theory in algebraic geometry involves watching a small deformation of one member of a family of objects, such as varieties, or subschemes in a fixed space, or vector bundles on a fixed scheme. In this new book, Robin Hartshorne studies first what happens over small infinitesimal deformations, and then gradually builds up to more global situations, using methods pioneered by Kodaira and Spencer in the complex analytic case, and adapted and expanded in algebraic geometry by Grothendieck. Topics include: * deformations over the dual numbers; * smoothness and the infinitesimal lifting property; * Zariski tangent space and obstructions to deformation problems; * pro-representable functors of Schlessinger; * infinitesimal study of moduli spaces such as the Hilbert scheme, Picard scheme, moduli of curves, and moduli of stable vector bundles. The author includes numerous exercises, as well as important examples illustrating various aspects of the theory. This text is based on a graduate course taught by the author at the University of California, Berkeley.
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