Nonabelian Jacobian of projective surfaces : geometry and representation theory /

Nonabelian Jacobian of projective surfaces : geometry and representation theory /

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Bibliographic Details
Author / Creator:Reider, Igor.
Imprint:Berlin : Springer, ©2013.
Description:1 online resource (viii, 214 pages).
Language:English
Series:Lecture notes in mathematics, 1617-9692 ; 2072
Lecture notes in mathematics (Springer-Verlag) ; 2072.
Subject:
Lie algebras.
Representations of algebras.
Lie algebras.
Representations of algebras.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11078240
Hidden Bibliographic Details
ISBN:9783642356629
3642356621
9783642356612
3642356613
Notes:Includes bibliographical references.
Online resource; title from PDF title page (SpringerLink, viewed Mar. 5, 2013).
Summary: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 invariantsof representation theoretic origin on smooth projective surfaces.
Other form:Printed edition: 9783642356612
Standard no.:10.1007/978-3-642-35662-9

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