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Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory
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 cla...
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| Auteur principal : | |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory / Igor Reider. |
| Édition : | 1st ed. 2013. |
| Publié : |
Berlin, Heidelberg :
Springer Berlin Heidelberg
, [20..] Cham : Springer Nature |
| Collection : | Lecture notes in mathematics (Internet) ; 2072 |
| Accès en ligne : |
Accès Nantes Université
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| Condition d'utilisation et de reproduction : | Conditions particulières de réutilisation pour les bénéficiaires des licences nationales : https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |
| Contenu : | 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 |
| Sujets : | |
| Documents associés : | Autre format:
Nonabelian Jacobian of projective surfaces Autre format: Nonabelian Jacobian of projective surfaces Autre format: Nonabelian Jacobian of Projective Surfaces |
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| 200 | 1 | |a Nonabelian Jacobian of Projective Surfaces |e Geometry and Representation Theory |f Igor Reider. | |
| 205 | |a 1st ed. 2013. | ||
| 214 | 0 | |a Berlin, Heidelberg |c Springer Berlin Heidelberg | |
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| 225 | 2 | |a Lecture Notes in Mathematics |x 1617-9692 |v 2072 | |
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| 327 | 1 | |a 1 Introduction |a 2 Nonabelian Jacobian J(X; L; d): main properties |a 3 Some properties of the filtration H |a 4 The sheaf of Lie algebras G |a 5 Period maps and Torelli problems |a 6 sl2-structures on F |a 7 sl2-structures on G |a 8 Involution on G |a 9 Stratification of T |a 10 Configurations and theirs equations |a 11 Representation theoretic constructions |a 12 J(X; L; d) and the Langlands Duality | |
| 330 | |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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| 452 | | | |0 168777878 |t Nonabelian Jacobian of projective surfaces |o geometry and representation theory |f Igor Reider |c Heidelberg |n Springer |d 2013 |p 1 vol. (VIII-214 p.) |s Lecture notes in mathematics |y 978-3-642-35661-2 | |
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