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 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}
}