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Book synopsis

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.

Book details

Book category Książki po angielsku Mathematics & science Mathematics Geometry

• Full title: Nonabelian Jacobian of Projective Surfaces
• Subtitle: Geometry and Representation Theory
• Author: Igor Reider
• Language: English
• Binding: Paperback
• Number of pages: 227
• EAN: 9783642356612
• ISBN: 3642356613
• ID: 01256006
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 350 g
• Dimensions: 236 × 158 × 13 mm
• Date of publishing: 15. March 2013

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