INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9783642356629
NATIONAL BIBLIOGRAPHY NUMBER
Country Code
IR
Number
EN-52329
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
انگلیسی
COUNTRY OF PUBLICATION OR PRODUCTlON
Country of publication
IR
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Nonabelian Jacobian of Projective Surface
General Material Designation
[Book]
Other Title Information
:Geometry and Representation Theory
First Statement of Responsibility
/ by Igor Reider
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Berlin, Heidelberg
Name of Publisher, Distributor, etc.
: Springer Berlin Heidelberg :Imprint: Springer,
Date of Publication, Distribution, etc.
, 2013.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
VIII, 227 p., online resource.
SERIES
Series Title
(Lecture Notes in Mathematics,0075-8434
Volume Designation
; 2072)
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
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.
Text of Note
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 sl2-structures on F -- 7 sl2-structures 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.?╗╣
SERIES
Title
Lecture Notes in Mathematics,0075-8434
Volume Number
2072
TOPICAL NAME USED AS SUBJECT
Mathematics
Geometry, algebraic
Matrix theory
Electronic books
LIBRARY OF CONGRESS CLASSIFICATION
Class number
E-BOOK
PERSONAL NAME - PRIMARY RESPONSIBILITY
Reider, Igor.
PERSONAL NAME - SECONDARY RESPONSIBILITY
SpringerLink (Online service)
ORIGINATING SOURCE
Country
ایران
ELECTRONIC LOCATION AND ACCESS
Host name
9783642356612.pdf
Access number
عادی
Compression information
عادی
Date and Hour of Consultation and Access
9783642356612.pdf
Electronic Format Type
متن
old catalog
e
BL
1
a
Y
