ENGLISH

Deformation theory

By Robin Hartshorne (auth.)

Book information

Publisher
Springer-Verlag New York
Year
2010
ISBN
1441915958, 9781441915955
DOI
10.1007/978-1-4419-1596-2
LCC
QA614.58 .H37 2010
Open Library ID
OL25147411M
Language
english
Format
PDF
Filesize
2 MB (1600039 bytes)
Series
Graduate Texts in Mathematics 257
Edition
1
Pages
234\241
Topic
Mathematics Algebra
Library
Kolxo3
Scanned
yes
Time added
2010-07-29 05:14:56
Algebraic Geometry

Description

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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