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

Santosha Kumar Pattanayak
(Chennai Mathematical Institute / IIT Kanpur)
Torsdag, 25 juni, 2015, at 15:15-16:15, in D03 (1531-019)
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(Vm)/W is projectively normal with respect to the descent of O(1)⊗|W|, where Vm denote the direct sum of m copies of V.
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen