Semiorthogonal decompositions of equivariant derived categories of invariant divisors

TL;DR

This paper develops a method to construct semiorthogonal decompositions of equivariant derived categories for invariant divisors, extending existing decompositions and providing new tools for understanding equivariant derived categories in algebraic geometry.

Contribution

It introduces a new construction of semiorthogonal decompositions for G-invariant divisors, building on previous work to analyze equivariant derived categories of smooth projective varieties.

Findings

Constructed semiorthogonal decompositions for G-invariant divisors.

Extended existing decompositions to new classes of equivariant derived categories.

Provided a framework for analyzing equivariant categories in algebraic geometry.

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.