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arXiv · 1709.10450

Semiorthogonal decompositions of equivariant derived categories of invariant divisors

Bronson Lim·Alexander Polishchuk
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Abstract

Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived categories of smooth varieties, we construct a similar semiorthogonal decomposition for a smooth $G$-invariant divisor in $X$ (under certain technical assumptions). Combining this procedure with the semiorthogonal decompositions constructed in [PV15], we construct semiorthogonal decompositions of some equivariant derived categories of smooth projective varieties.

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Bronson Lim, Alexander Polishchuk. 2019-09-06. Semiorthogonal decompositions of equivariant derived categories of invariant divisors. https://arxiv.org/abs/1709.10450

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