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...
Gardado en:
| Autor Principal: | |
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| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2013. |
| Series: | Lecture Notes in Mathematics
2072 |
| Sujets: | |
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 220 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Nonabelian Jacobian of projective surfaces, geometry and representation theory, Igor Reider, Heidelberg, Springer, 2013, 1 vol. (VIII-214 p.), Lecture notes in mathematics, 978-3-642-35661-2 • Nonabelian Jacobian of projective surfaces, geometry and representation theory, Igor Reider, Heidelberg, Springer, 2013, 1 vol. (VIII-214 p.), Lecture notes in mathematics, 978-3-642-35661-2 • Nonabelian Jacobian of Projective Surfaces, Texte imprimé, 9783642356636 |
| 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 |
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| descrición da copia: | L'impression du document génère 220 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografía: | Bibliogr. |
| ISBN: | 9783642356629 |
| ISSN: | 1617-9692 |
| Acceso: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |