Mathematical Research Letters

Volume 27 (2020)

Number 5

Semiorthogonal decompositions of equivariant derived categories of invariant divisors

Pages: 1465 – 1498



Bronson Lim (Department of Mathematics, University of Utah, Salt Lake City, Ut., U.S.A.)

Alexander Polishchuk (Department of Mathematics, University of Oregon, Eugene, Or., U.S.A.)


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 [18], we construct semiorthogonal decompositions of some equivariant derived categories of smooth projective hypersurfaces.

Received 21 November 2017

Accepted 29 March 2020

Published 12 January 2021