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3264 and All That | Hodge Theory and Complex Algebraic Geometry II | Algebraic Geometry | D-Modules, Perverse Sheaves, And Representation Theory | Complex Manifolds And Deformation Of Complex Structures | Commutative Algebra With a View Toward Algebraic Geometry | Lectures on K3 Surfaces
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.
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.
About: 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.
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