ACM bundles on cubic threefolds

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.

40 pages. The previous version contained a typo in the name of the first author, which has been corrected. This paper consists of the first three sections of the previous version of arXiv:1303.6998 which was split into two different papers. Final version to appear in Algebraic Geometry

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• ACM bundles on del Pezzo surfaces
• n-dimensional Fano varieties of wild representation type
• Theta-duality on Prym varieties and a Torelli Theorem