On intersection cohomology with torus actions of complexity one

Marta Agustin Vicente; Kevin Langlois

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arXiv · 1412.7634

On intersection cohomology with torus actions of complexity one

Marta Agustin Vicente·Kevin Langlois

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Abstract

The purpose of this article is to investigate the intersection cohomology for algebraic varieties with torus action. Given an algebraic torus $\mathbb{T}$, one of our result determines the intersection cohomology Betti numbers of any normal projective $\mathbb{T}$-variety admitting an algebraic curve as global quotient. The calculation is expressed in terms of a combinatorial description involving a divisorial fan which is the analogous of the defining fan of a toric variety. Our main tool to obtain this computation is a description of the decomposition theorem in this context.

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Marta Agustin Vicente, Kevin Langlois. 2014-12-24. On intersection cohomology with torus actions of complexity one. https://arxiv.org/abs/1412.7634

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