English

Lines on cubic threefolds and fourfolds containing a plane

Algebraic Geometry 2023-06-13 v2

Abstract

We describe the Fano scheme of lines on a general cubic threefold containing a plane over a field kk of characteristic different from 2. Then, we use the Fano scheme to characterize rationality for such cubic threefolds over nonclosed fields and to construct a Lagrangian fibration from the Fano variety of lines on a cubic fourfold containing a plane explicitly.

Keywords

Cite

@article{arxiv.2211.13444,
  title  = {Lines on cubic threefolds and fourfolds containing a plane},
  author = {Corey Brooke},
  journal= {arXiv preprint arXiv:2211.13444},
  year   = {2023}
}
R2 v1 2026-06-28T07:11:07.706Z