Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz
We calculate the E -polynomials of certain twisted GL( n ,ℂ)-character varieties of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric resu...
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| Veröffentlicht in: | Inventiones mathematicae 2008-12, Vol.174 (3), p.555-624 |
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| creator | Hausel, Tamás Rodriguez-Villegas, Fernando |
| description | We calculate the
E
-polynomials of certain twisted GL(
n
,ℂ)-character varieties
of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type
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
: 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. |
| doi_str_mv | 10.1007/s00222-008-0142-x |
| format | Article |
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E
-polynomials of certain twisted GL(
n
,ℂ)-character varieties
of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type
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
: 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
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E
-polynomials of certain twisted GL(
n
,ℂ)-character varieties
of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type
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
: 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
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E
-polynomials of certain twisted GL(
n
,ℂ)-character varieties
of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lie-type
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
: 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
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| ispartof | Inventiones mathematicae, 2008-12, Vol.174 (3), p.555-624 |
| issn | 0020-9910 1432-1297 |
| language | eng |
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| source | SpringerNature Journals |
| subjects | Mathematics Mathematics and Statistics |
| title | Mixed Hodge polynomials of character varieties: With an appendix by Nicholas M. Katz |
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