Deformation Theory Hardcover - 2009 - 2010th Edition
by Robin Hartshorne
From the rear cover
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.
Details
- Title Deformation Theory
- Author Robin Hartshorne
- Binding Hardcover
- Edition number 2010th
- Edition 2010
- Pages 234
- Volumes 1
- Language ENG
- Publisher Springer, USA
- Date 2009-12-10
- Illustrated Yes
- Features Bibliography, Illustrated, Index
- ISBN 9781441915955 / 1441915958
- Weight 1.14 lbs (0.52 kg)
- Dimensions 9.21 x 6.14 x 0.56 in (23.39 x 15.60 x 1.42 cm)
-
Themes
- Aspects (Academic): Science/Technology Aspects
- Library of Congress subjects Geometry, Algebraic, Deformations of singularities
- Library of Congress Catalog Number 2009939327
- Dewey Decimal Code 516.35
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