English

The Fermat cubic and monodromy of lines

Algebraic Geometry 2023-02-21 v1

Abstract

In this paper we study properties of the locus of second type lines of a general cubic threefold and fourfold. By analysing the geometry of the Fano scheme of lines of the Fermat cubic fourfold and in particular giving an explicit description of the locus of second type lines, we deduce that the Voisin map is birational over the second type locus. For a general cubic threefold, by studying properties of the second type locus again, we compute that various natural geometric monodromy groups are the full symmetric group.

Keywords

Cite

@article{arxiv.2302.09562,
  title  = {The Fermat cubic and monodromy of lines},
  author = {Frank Gounelas and Alexis Kouvidakis},
  journal= {arXiv preprint arXiv:2302.09562},
  year   = {2023}
}