Generalized twisted cubics on a cubic fourfold as a moduli space of stable objects

Martí Lahoz, Manfred Lehn, Emanuele Macrì, Paolo Stellari

Published 2016-09-15Version 1

We revisit the work of Lehn-Lehn-Sorger-van Straten on twisted cubic curves in a cubic fourfold in terms of moduli spaces of Gieseker stable sheaves. We show that the irreducible holomorphic symplectic eightfold associated to a cubic fourfold not containing a plane and described by the four authors is birational to a moduli space of stable aCM bundles on the cubic fourfold itself. For a very general such cubic fourfold, we show that the eightfold is isomorphic to a moduli space of tilt-stable objects in the derived category. Finally, the blow-up of this eightfold along the cubic fourfold is then described as a moduli space of rank 3 Gieseker stable torsion free sheaves.