Title: |
Projective normality of GIT Quotient Varieties modulo Finite Group Actions. |

Speaker: |
S. Senthamarai Kannan (Chennai and 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. |