Deformation theory
By: Robin Hartshorne
Series: Graduate texts in mathematics -- 257; Graduate texts in mathematics -- 257.
Publisher: Springer
Published: 2010
Place of publication: New York
Language: eng
Number of pages: 234
ISBN-13: 9781441915955; 9781441915962
Subjects: Deformations of singularities; Algebraic Geometry; Deformation <Mathematik>
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."--
Notes: Includes bibliographical references (p. [217]-224) and index.