Nonabelian Jacobian of Projective Surfaces - Geometry and Representation Theory (Paperback, 2013 ed.)

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.

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Lecture Notes in Mathematics, 2072
Release date:	March 2013
First published:	2013
Authors:	Igor Reider
Dimensions:	235 x 155 x 13mm (L x W x T)
Format:	Paperback
Pages:	227
Edition:	2013 ed.
ISBN-13:	978-3-642-35661-2
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General Books > Science & Mathematics > Mathematics > Geometry > Algebraic geometry Promotions
LSN:	3-642-35661-3
Barcode:	9783642356612

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