Derived symmetries for crepant contractions to hypersurfaces

Abstract

Given a crepant contraction f to a singularity X, we may expect a derived symmetry of the source of f. Under easily-checked geometric assumptions, I construct such a symmetry when X is a hypersurface in a smooth ambient S, using a spherical functor from the derived category of S. I describe this symmetry, relate it to other symmetries, and establish its compatibility with base change.

Streamlined exposition. 35 pages, 3 figures