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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Moduli Spaces of Gorenstein Quasi-Homogenous Surfa
ce Singularities - Pratoussevitch\, A (Liverpool)
DTSTART;TZID=Europe/London:20110125T100000
DTEND;TZID=Europe/London:20110125T110000
UID:TALK29663AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/29663
DESCRIPTION:Gorenstein quasi-homogeneous surface singularities
\, studied by Dolgachev\, Neumann and others\, cor
respond to lifts of Fuchsian groups into the unive
rsal covering of PSL(2\,R). I will show that the s
pace of Gorenstein quasi-homogeneous surface singu
larities corresponding to a certain Fuchsian group
is a finite affine space of Z/mZ-valued functions
on the Fuchsian group\, called m-Arf functions. U
sing m-Arf functions\, I will count connected comp
onents of the space of Gorenstein quasi-homogeneou
s surface singularities and prove that any connect
ed component is homeomorphic to a quotient of R^d
by a discrete group. This work is connected to the
earlier results of Atiyah and Mumford on spin str
uctures on compact Riemann surfaces and of Jarvis\
, Kimura and Vaintrob on moduli spaces of higher s
pin curves. This is joint work with Sergey Natanzo
n.\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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