Derived Autoequivalences of Bielliptic Surfaces

TL;DR

This paper characterizes the group of autoequivalences of the derived category of bielliptic surfaces by analyzing their action on the numerical Grothendieck group, providing insights into their symmetries.

Contribution

It offers a detailed description of the autoequivalence group for bielliptic surfaces, a previously less understood class of algebraic surfaces.

Findings

Identified the structure of the autoequivalence group

Connected autoequivalences to actions on the numerical Grothendieck group

Enhanced understanding of symmetries in derived categories of bielliptic surfaces

Abstract

We describe the group of exact autoequivalences of the bounded derived category of coherent sheaves on a bielliptic surface. We achieve this by studying its action on the numerical Grothendieck group of the surface.