{"product_id":"nonabelian-jacobian-of-projective-surfaces-geometry-and-representation-theory-von-igor-reider","title":"Nonabelian Jacobian of Projective Surfaces","description":"The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras\/groups. This work’s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using the representation theory to systematically address various algebro-geometric problems. It also shows how to construct new invariants of representation theoretic origin on smooth projective surfaces.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642356612\"\u003e\u003ch3\u003eGeometry and Representation Theory\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642356612","offer_id":39429734793309,"sku":"9783642356612","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/2d257032-99ee-4eac-9e90-8ba724e6cace.jpg?v=1772174987","url":"https:\/\/shop.autorenwelt.de\/en\/products\/nonabelian-jacobian-of-projective-surfaces-geometry-and-representation-theory-von-igor-reider","provider":"Autorenwelt Shop","version":"1.0","type":"link"}