Nonabelian Jacobian of Projective Surfaces (Record no. 31309)
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000 -LEADER | |
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fixed length control field | 03341nam a22004815i 4500 |
020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
ISBN | 9783642356629 |
-- | 978-3-642-35662-9 |
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
Classification number | 516.35 |
100 1# - MAIN ENTRY--AUTHOR NAME | |
Personal name | Reider, Igor. |
245 10 - TITLE STATEMENT | |
Title | Nonabelian Jacobian of Projective Surfaces |
Sub Title | Geometry and Representation Theory / |
Statement of responsibility, etc | by Igor Reider. |
260 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
Place of publication | Berlin, Heidelberg : |
Name of publisher | Springer Berlin Heidelberg : |
-- | Imprint: Springer, |
Year of publication | 2013. |
300 ## - PHYSICAL DESCRIPTION | |
Number of Pages | VIII, 227 p. |
Other physical details | online resource. |
490 1# - SERIES STATEMENT | |
Series statement | Lecture Notes in Mathematics, |
505 0# - FORMATTED CONTENTS NOTE | |
Formatted contents 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. |
520 ## - SUMMARY, ETC. | |
Summary, etc | 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. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Mathematics. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Geometry, algebraic. |
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Matrix theory. |
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Mathematics. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Algebraic Geometry. |
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
Topical Term | Linear and Multilinear Algebras, Matrix Theory. |
856 40 - ELECTRONIC LOCATION AND ACCESS | |
Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-642-35662-9 |
942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
Koha item type | E-BOOKS |
264 #1 - | |
-- | Berlin, Heidelberg : |
-- | Springer Berlin Heidelberg : |
-- | Imprint: Springer, |
-- | 2013. |
336 ## - | |
-- | text |
-- | txt |
-- | rdacontent |
337 ## - | |
-- | computer |
-- | c |
-- | rdamedia |
338 ## - | |
-- | online resource |
-- | cr |
-- | rdacarrier |
347 ## - | |
-- | text file |
-- | |
-- | rda |
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
-- | 0075-8434 ; |
Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Accession Number | Uniform Resource Identifier | Koha item type |
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IMSc Library | EBK2015 | http://dx.doi.org/10.1007/978-3-642-35662-9 | E-BOOKS |