ACM bundles on cubic threefolds

TL;DR

This paper investigates ACM bundles on cubic threefolds using derived category methods, establishing the non-emptiness of moduli spaces of stable Ulrich bundles and describing their birational relations via wall-crossing.

Contribution

It demonstrates the non-emptiness of moduli spaces of stable Ulrich bundles on cubic threefolds and characterizes their birational structure through Bridgeland stability wall-crossing.

Findings

Moduli space of stable Ulrich bundles is always non-empty.

Birational equivalence to moduli of semistable torsion sheaves on P^2 with Clifford algebra action.

Wall-crossing describes the birational isomorphism for instanton sheaves.

Abstract

We study ACM bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion sheaves on the projective plane endowed with the action of a Clifford algebra. We describe this birational isomorphism via wall-crossing in the space of Bridgeland stability conditions, in the example of instanton sheaves of minimal charge.