Derived symmetries for crepant contractions to hypersurfaces

TL;DR

This paper constructs a derived symmetry for crepant contractions to hypersurface singularities using spherical functors, relating it to other symmetries and ensuring compatibility with base change.

Contribution

It introduces a new derived symmetry construction for crepant contractions to hypersurfaces, expanding understanding of symmetries in algebraic geometry.

Findings

Constructed a derived symmetry using spherical functors.

Related the new symmetry to existing symmetries.

Proved compatibility with base change.

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.