Description 
1 online resource (vi, 234 pages) : illustrations 
Series 
Graduate texts in mathematics, 00725285 ; 257 

Graduate texts in mathematics ; 257.

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; * prorepresentable 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 
Bibliography 
Includes bibliographical references (pages 217224) and index 
Notes 
Print version record 
Subject 
Deformations of singularities.


Geometry, Algebraic.


Deformations of singularities.


Geometry, Algebraic.

Genre/Form 
Electronic books

Form 
Electronic book

ISBN 
9781441915962 

1441915966 
