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arXiv · 2412.19787

Perverse sheaves on smooth toric varieties and stacks

Sergey Guminov
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Abstract

It is usually not straightforward to work with the category of perverse sheaves on a variety using only its definition as a heart of a $t$-structure. In this paper, the category of perverse sheaves on a smooth toric variety with its orbit stratification is described explicitly as a category of finite-dimensional modules over an algebra. An analogous result is also established for various categories of equivariant perverse sheaves, which in particular gives a description of perverse sheaves on toric orbifolds, and we also compare the derived category of the category of perverse sheaves to the derived category of constructible sheaves.

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Sergey Guminov. 2024-12-27. Perverse sheaves on smooth toric varieties and stacks. https://arxiv.org/abs/2412.19787

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