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

Santosha Kumar Pattanayak
(Chennai Mathematical Institute / IIT Kanpur)
Seminar
Torsdag, 25 juni, 2015, at 15:15-16:15, in D03 (1531-019)
Abstrakt:

We prove that for any finite dimensional vector space $V$ over an algebraically closed field $K$, and for any finite subgroup $G$ of $\mathrm{GL}(V)$ 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 $O(1)\otimes|G|$, where $O(1)$ denotes the ample generator of the Picard group of $\mathbb{P}(V)$. 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 $\mathbb{C}$, the projective variety $\mathbb{P}(Vm)/W$ is projectively normal with respect to the descent of $O(1)\otimes|W|$, where $Vm$ denote the direct sum of $m$ copies of $V$.

Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen