Autoequivalences of Derived Categories of Bielliptic Surfaces

TL;DR

This paper characterizes the autoequivalence group of derived categories for bielliptic surfaces and shows derived equivalence implies isomorphism for these surfaces.

Contribution

It explicitly determines the autoequivalence group for bielliptic surfaces and proves derived equivalence implies isomorphism for these surfaces.

Findings

The autoequivalence group generators are explicitly identified.

Derived equivalence to a bielliptic surface implies the surfaces are isomorphic.

Results hold over algebraically closed fields of any characteristic.

Abstract

We determine the generators of the autoequivalence group of the derived category of coherent sheaves on a bielliptic surface over an algebraically closed field of arbitrary characteristic. As a consequence, we prove that any algebraic variety derived equivalent to such a surface is isomorphic to the surface itself.