{"product_id":"9783642356612","title":"Nonabelian Jacobian of Projective Surfaces: Geometry and Representation Theory","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.","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":46412585009393,"sku":"9783642356612","price":54.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0674\/5433\/7265\/files\/9783642356612_p0.jpg?v=1765324734","url":"https:\/\/shop.barnesandnoble.com\/products\/9783642356612","provider":"Barnes \u0026 Noble","version":"1.0","type":"link"}