Some non-special cubic fourfolds
Algebraic Geometry
2018-11-06 v2
Abstract
In [1309.1899], Ranestad and Voisin showed, quite surprisingly, that the divisor in the moduli space of cubic fourfolds consisting of cubics "apolar to a Veronese surface" is not a Noether-Lefschetz divisor. We give an independent proof of this by exhibiting an explicit cubic fourfold X in the divisor and using point counting methods over finite fields to show X is Noether-Lefschetz general. We also show that two other divisors considered in [ibid.] are not Noether-Lefschetz divisors.
Keywords
Cite
@article{arxiv.1703.05923,
title = {Some non-special cubic fourfolds},
author = {Nicolas Addington and Asher Auel},
journal= {arXiv preprint arXiv:1703.05923},
year = {2018}
}
Comments
13 pages, Macaulay2 and C++ code as ancillary files. Minor changes, to appear in Documenta Math