On the symplectic eightfold associated to a Pfaffian cubic fourfold
Algebraic Geometry
2018-03-12 v2
Abstract
We show that the irreducible holomorphic symplectic eightfold Z associated to a cubic fourfold Y not containing a plane is deformation-equivalent to the Hilbert scheme of four points on a K3 surface. We do this by constructing for a generic Pfaffian cubic Y a birational map Z ---> Hilb^4(X), where X is the K3 surface associated to Y by Beauville and Donagi. We interpret Z as a moduli space of complexes on X and observe that at some point of Z, hence on a Zariski open subset, the complex is just the ideal sheaf of four points.
Keywords
Cite
@article{arxiv.1404.5657,
title = {On the symplectic eightfold associated to a Pfaffian cubic fourfold},
author = {N. Addington and M. Lehn},
journal= {arXiv preprint arXiv:1404.5657},
year = {2018}
}
Comments
9 pages. Minor changes; to appear in Crelle as an appendix to 1305.0178