$q$-bic threefolds and their surface of lines
Algebraic Geometry
2026-03-10 v1 Number Theory
Representation Theory
Abstract
For any power of the positive ground field characteristic, a smooth -bic threefold -- the Fermat threefold of degree for example -- has a smooth surface of lines which behaves like the Fano surface of a smooth cubic threefold. I develop projective, moduli-theoretic, and degeneration techniques to study the geometry of . Using, in addition, the modular representation theory of the finite unitary group and the geometric theory of filtrations, I compute cohomology of the structure sheaf of when is prime.
Cite
@article{arxiv.2402.09884,
title = {$q$-bic threefolds and their surface of lines},
author = {Raymond Cheng},
journal= {arXiv preprint arXiv:2402.09884},
year = {2026}
}
Comments
47 pages. Comments very welcome!