Hidden Bibliographic Details
| ISBN: | 9783642356629
3642356621
9783642356612
3642356613
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| Notes: | Includes bibliographical references.
Online resource; title from PDF title page (SpringerLink, viewed Mar. 5, 2013).
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| Summary: | 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 invariantsof representation theoretic origin on smooth projective surfaces.
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| Other form: | Printed edition: 9783642356612
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| Standard no.: | 10.1007/978-3-642-35662-9
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