{"product_id":"9781461425205","title":"Deformation Theory","description":"\u003cp\u003eThe 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.\u003c\/p\u003e\u003cp\u003eThis include:\u003c\/p\u003e\u003cp\u003edeformations over the dual numbers\u003c\/p\u003e\u003cp\u003esmoothness and the infinitesimal lifting property\u003c\/p\u003e\u003cp\u003eZariski tangent space and obstructions to deformation problems\u003c\/p\u003e\u003cp\u003epro-representable functors of Schlessinger\u003c\/p\u003e\u003cp\u003einfinitesimal study of moduli spaces such as the Hilbert scheme, Picard scheme, moduli of curves, and moduli of stable vector bundles.\u003c\/p\u003e\u003cp\u003eThe author includes numerous exercise, 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.  \u003c\/p\u003e","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":47060836352240,"sku":"9781461425205","price":69.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781461425205_p0.jpg?v=1763691488","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781461425205","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}