English

On two rationality conjectures for cubic fourfolds

Algebraic Geometry 2016-08-18 v4

Abstract

Motivated by the question of rationality of cubic fourfolds, we show that a cubic X has an associated K3 surface in the sense of Hassett if and only if the variety F of lines on X is birational to a moduli space of sheaves on a K3 surface, but that having F birational to Hilb^2(K3) is more restrictive. We compare the loci in the moduli space of cubics where each condition is satisfied.

Keywords

Cite

@article{arxiv.1405.4902,
  title  = {On two rationality conjectures for cubic fourfolds},
  author = {Nicolas Addington},
  journal= {arXiv preprint arXiv:1405.4902},
  year   = {2016}
}

Comments

10 pages; final version to appear in Math. Res. Lett

R2 v1 2026-06-22T04:18:25.668Z