| Nonabelian Jacobian of Projective Surfaces: Geometry and Representation Theory 2013 Edition Contributor(s): Reider, Igor (Author) |
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ISBN: 3642356613 ISBN-13: 9783642356612 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: March 2013 |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Mathematics | Geometry - Algebraic |
| Dewey: 512.5 |
| Series: Lecture Notes in Mathematics |
| Physical Information: 0.48" H x 6.14" W x 9.21" (0.71 lbs) 227 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |