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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Hodge polynomials of the moduli space of SL (2\,C)
- character varieties - Logares\, M (ICMAT)
DTSTART;TZID=Europe/London:20110203T153000
DTEND;TZID=Europe/London:20110203T163000
UID:TALK29649AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29649
DESCRIPTION:Let X be a compact Riemann surface of genus g. SL
(2\,C)-character varieties of X are rich objects w
hich lie in the intersection of algebraic geometry
\, complex geometry\, and differential geometry. W
hile they are diffeomorphic to moduli spaces of Hi
ggs bundles\, as algebraic varieties they are very
different. Character varieties are affine\, while
Higgs moduli spaces are foliated by the fibers of
the Hitchin map which are compact algebraic subva
rieties. There has been much work investigating th
e mixed Hodge structures on the cohomology groups
of these character varieties\, and their Hodge pol
ynomials have been computed using number theoretic
al techniques.\n\nOur goal is to compute the Hodge
polynomial of SL(2\,C)-character varieties\, by s
tratifying these spaces in such a way that Hodge s
tructure theory gives simpler formulas for the str
ata\, so we are allowed to compute the whole polyn
omials in terms of the Hodge polynomials of the st
rata. This is work in progress with V. Muoz and P.
Newstead.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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