ACM bundles on cubic fourfolds containing a plane

Abstract

We study ACM bundles on cubic fourfolds containing a plane exploiting the geometry of the associated quadric fibration and Kuznetsov's treatment of their bounded derived categories of coherent sheaves. More precisely, we recover the K3 surface naturally associated to the fourfold as a moduli space of Gieseker stable ACM bundles of rank four.

18 pages. This is the last section of the previous version of arXiv:1303.6998 which is now spit into two parts. Explanations added

References in corpus (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Hodge theory and derived categories of cubic fourfolds
• Instanton bundles on Fano threefolds
• ACM bundles on del Pezzo surfaces
• The Derived Category of the Intersection of Four Quadrics
• Projectivity and Birational Geometry of Bridgeland moduli spaces
• Stable Ulrich bundles
• Theta-duality on Prym varieties and a Torelli Theorem
• Stability conditions and extremal contractions

Cited by in corpus (4)

• On the symplectic eightfold associated to a Pfaffian cubic fourfold
• Compactification of the moduli space of instanton sheaves on the Fano threefold $V_5$
• Fano visitors, Fano dimension and orbifold Fano hosts
• Gepner type stability condition via Orlov/Kuznetsov equivalence