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|a 9783642356629
|9 978-3-642-35662-9
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|a 10.1007/978-3-642-35662-9
|2 doi
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|a QA564-609
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|a PBMW
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|a MAT012010
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|a Reider, Igor.
|e author.
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|a Nonabelian Jacobian of Projective Surfaces
|b Geometry and Representation Theory /
|c by Igor Reider.
|h [electronic resource] :
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 2013.
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|a VIII, 227 p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
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|2 rdamedia
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|a online resource
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|v 2072
|x 0075-8434 ;
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|a 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.
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|a 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.
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|a Mathematics.
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|a Geometry, algebraic.
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|a Matrix theory.
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|a Mathematics.
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|a Algebraic Geometry.
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|a Linear and Multilinear Algebras, Matrix Theory.
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783642356612
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| 830 |
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|a Lecture Notes in Mathematics,
|v 2072
|x 0075-8434 ;
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-35662-9
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a Mathematics and Statistics (Springer-11649)
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