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OverviewThe 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. Full Product DetailsAuthor: Robin HartshornePublisher: Springer Imprint: Springer Dimensions: Width: 23.40cm , Height: 1.30cm , Length: 15.60cm Weight: 0.345kg ISBN: 9781441916136ISBN 10: 144191613 Pages: 244 Publication Date: 13 November 2009 Audience: General/trade , General Format: Undefined Publisher's Status: Unknown Availability: Out of stock ![]() Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |