Global topology of the Hitchin system

Details Global topology of the Hitchin system Global topology of the Hitchin system

2011-02-08

arxiv.org/abs/1102.1717v2

Mathematics

Algebraic Geometry

41 pages, small changes and clarifications, to appear in Handbook of Moduli

Scientific paper

Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory.

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