# Seminar by Santosha Kumar Pattanayak (CMI / IIT Kanpur)

Title: Projective Normality of G.I.T. quotient varieties modulo finite groups

2015.06.19 | Jane Jamshidi

 Date Thu 25 Jun Time 15:15 — 16:15 Location 1531-019 (D-03)

We prove that for any finite dimensional vector space V over an algebraically closed field K, and for any finite subgroup G of GL(V) which is either solvable or is generated by pseudo reflections such that the |G| is a unit in K, the projective variety P(V)/G is projectively normal with respect to the descent of O(1)|G|, where O(1) denotes the ample generator of the Picard group of ℙ(V). We also prove that for the standard representation V of the Weyl group W of a semi-simple algebraic group of type An,Bn,Cn,Dn, F4 and G2 over ℂ, the projective variety ℙ(m)/W is projectively normal with respect to the descent of O(1)⊗|W|, where m denote the direct sum of copies of V.

IT, computer science and mathematics