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Deformation Theory / Robin Hartshorne

By: Hartshorne, RobinContributor(s): Hartshorne, RobinMaterial type: Text

TextPublisher number: :International Book Distributors | ;Flat No 17, Prakash Aaprtment 4405/2, 5 Ansari Road Darya Ganj New Delhi Series: Graduate texts in mathematics, 257Publication details: New York : Springer, ©2010Description: vi, 234p. 24cmISBN: 9781441915955Subject(s): Mathematics | Geometry | Geometry, Algebraic | Deformations of singularities | Geometrie algeebriqueDDC classification: 516.35 HAR

Contents:

Preface -- Getting Started -- Higher Order Deformations -- Formal Moduli -- Global Questions -- References.

Summary: 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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Holdings
Item type	Current library	Call number	Status	Notes	Date due	Barcode	Item holds
Books	SNU LIBRARY	516.35 HAR (Browse shelf(Opens below))	Not For Loan	Books Shifted in Mathematics Dept.		28788

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Previous	516.35 HAR Algebraic Geometry: A First Course	516.35 HAR Algebraic Geometry	516.35 HAR Algebraic Geometry	516.35 HAR Deformation Theory	516.35 HIT Integrable Systems	516.35 KEM Complex abelian varieties and theta functions.	516.35 KOB Introduction to Elliptic Curves and Modular Forms	Next

Preface --
Getting Started --
Higher Order Deformations --
Formal Moduli --
Global Questions --
References.

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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