School Seminars and Colloquia

Projective normality of GIT Quotient Varieties modulo Finite Group Actions

Algebra/Geometry/Topology Seminar

by Prof S Senthamarai Kannan

Institution: Chennai Mathematical Institute
Date: Mon 26th July 2010
Time: 2:15 PM
Location: Old Arts B, The University of Melbourne

Abstract: Let G be a finite group of order n. Let V be a finite dimensional representation of G over an algebraically closed field whose characteristic does not divide n. Then, the line bundle O(1)^{\otimes n} on the projective space P(V) descends to the quotient G\P(V). On the other hand G\V is normal. So, it is a natural question to ask whether the polarised Variety (G\P(V), L) is projective normal, where L denotes the descent of the line bundle on G\P(V) given by the descent of O(1)^{\otimes n}). In this talk we give an affirmative anwer to this question when G is solvable or for certain representations of Weyl groups. We also give a connection between this question to a Combinatorial result due to Erdos-Ginzburg-Ziv.

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