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 (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
• Derived categories of cubic fourfolds
• Instanton bundles on Fano threefolds
• ACM bundles on del Pezzo surfaces
• Espace des modules des faisceaux semi-stables de rang 2 et de classes de Chern $c_1=0$, $c_2=2$ et $c_3=0$ sur une hypersurface cubique lisse de ${\mathbb{P}}^4$
• Minimal sections of conic bundles
• n-dimensional Fano varieties of wild representation type
• Theta-duality on Prym varieties and a Torelli Theorem

Cited by in corpus (4)

• Stability conditions on Kuznetsov components
• Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$
• Bridgeland stability of minimal instanton bundles on Fano threefolds
• Bridgeland Moduli spaces for Gushel-Mukai threefolds and Kuznetsov's Fano threefold conjecture