Betti numbers of GIT quotients of products of projective planes

Details Betti numbers of GIT quotients of products of projective planes Betti numbers of GIT quotients of products of projective planes

2009-03-30

arxiv.org/abs/0903.5235v2

Mathematics

Algebraic Geometry

14 pages

Scientific paper

We study the GIT quotients for the diagonal action of the algebraic group $SL_3(\mathbb{C})$ on the $n$-fold product of $\mathbb{P}^2(\mathbb{C})$: in particular we determine a strategy in order to determine the (intersection) Poincar\'{e} polynomial of any quotient variety. In the special case $n=6$ we determine an explicit formula for the (intersection) Betti numbers of a quotient variety, depending only on the combinatorics of the weights of the polarization $m\in \mathbb{Z}^6_{>0}$.

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