Nonabelian Jacobian of projective surfaces geometry and representation theory Igor Reider

Format:

Book

Author/Creator:

Reider, Igor

Series:

Lecture notes in mathematics (Springer-Verlag) 2072

Lecture notes in mathematics 1617-9692 2072

Language:

English

Subjects (All):

Lie algebras.

Representations of algebras.

Physical Description:

1 online resource

Place of Publication:

Berlin Springer ©2013

Language Note:

English

System Details:

text file

PDF

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

Contents:

Introduction Nonabelian Jacobian J(X; L, d): Main Properties Some Properties of the Filtration H̃ _ The Sheaf of Lie Algebras G[gamma] Period Maps and Torelli Problems sl₂-Structures on F' sl₂-Structures on G[gamma] Involution on G[gamma] Stratification of T [pi] Configurations and Theirs Equations Representation Theoretic Constructions J(X; L, d) and the Langlands Duality

Notes:

Includes bibliographical references

Online resource; title from PDF title page (SpringerLink, viewed March 5, 2013)

Other Format:

Printed edition:

ISBN:

9783642356629

3642356621

OCLC:

828879860

Access Restriction:

Restricted for use by site license