| 书目名称 | Nonabelian Jacobian of Projective Surfaces |
| 副标题 | Geometry and Represe |
| 编辑 | Igor Reider |
| 视频video | |
| 概述 | Includes supplementary material: |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | 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 theore |
| 出版日期 | Book 2013 |
| 关键词 | 14J60,14C05,16G30; Lie algebra; surfaces; vector bundles; zero-cycles; matrix theory |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-642-35662-9 |
| isbn_softcover | 978-3-642-35661-2 |
| isbn_ebook | 978-3-642-35662-9Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | Springer-Verlag Berlin Heidelberg 2013 |
发表于 2025-3-21 16:08:54
