Nonabelian Jacobian of projective surfaces : geometry and representation theory
 Responsibility
 Igor Reider.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2013.
 Physical description
 viii, 214 p. : ill. ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2072.
Access
Creators/Contributors
 Author/Creator
 Reider, Igor.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 213214).
 Contents

 1 Introduction. 2 Nonabelian Jacobian J(X L d): main properties. 3 Some properties of the filtration H. 4 The sheaf of Lie algebras G. 5 Period maps and Torelli problems. 6 sl2structures on F.7 sl2structures on G. 8 Involution on G. 9 Stratification of T.10 Configurations and theirs equations. 11 Representation theoretic constructions. 12 J(X L d) and the Langlands Duality.
 (source: Nielsen Book Data)
 Publisher's 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 Hodgelike 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 indepth 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 algebrogeometric problems. It also shows how to construct new invariants of representation theoretic origin on smooth projective surfaces.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2013
 Series
 Lecture notes in mathematics ; 2072
 ISBN
 3642356613
 9783642356612