Nantilus
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...
Enregistré dans:
| 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
Accès direct soit depuis les campus via le réseau ou le wifi eduroam soit à distance avec un compte @etu.univ-nantes.fr ou @univ-nantes.fr |
| Note sur l'URL : | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex |
| 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 |
| Résumé : | 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 |
|---|---|
| Notes : | L'impression du document génère 220 p. |
| Bibliographie : | Bibliogr. |
| ISBN : | 978-3-642-35662-9 |
| DOI : | 10.1007/978-3-642-35662-9 |