# 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.

*For More Information:* contact: Arun Ram. email: aram@unimelb.edu.au