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arXiv · 0903.5235

Betti numbers of GIT quotients of products of projective planes

Francesca Incensi
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Abstract

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) Poincaré 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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BibTeXRIS

Francesca Incensi. 2009-11-24. Betti numbers of GIT quotients of products of projective planes. https://arxiv.org/abs/0903.5235

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