Journal article
Mixed Hodge polynomials of character varieties
- Abstract:
- We calculate the E-polynomials of certain twisted GL(n,C)-character varieties M_n of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type GL(n,F_q) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,C)-character variety. The calculation also leads to several conjectures about the cohomology of M_n: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain quiver. We prove these conjectures for n = 2.
- Publication status:
- Published
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- Publisher copy:
- 10.1007/s00222-008-0142-x
Authors
- Journal:
- INVENTIONES MATHEMATICAE More from this journal
- Volume:
- 174
- Issue:
- 3
- Pages:
- 555-624
- Publication date:
- 2006-12-21
- DOI:
- EISSN:
-
1432-1297
- ISSN:
-
0020-9910
- Keywords:
- Pubs id:
-
pubs:4680
- UUID:
-
uuid:f48eb3db-4fc3-449f-94b1-2d3f3622706d
- Local pid:
-
pubs:4680
- Source identifiers:
-
4680
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright date:
- 2006
- Notes:
-
with an appendix by Nicholas M. Katz; 57 pages. revised version: New
definition for homogeneous weight in Definition 4.1.6, subsequent arguments
modified. Some other minor changes. To appear in Invent. Math
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