Cubic Surfaces of Characteristic Two
Commutative Algebra
2022-05-16 v2 Algebraic Geometry
Abstract
Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that, the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the 19-dimensional space of all cubics, and that up to projective equivalence, there are finitely many non-Frobenius split cubic surfaces. We explicitly describe defining equations for each and characterize them as extremal in terms of configurations of lines on them. In particular, a (possibly singular) cubic surface in characteristic two fails to be Frobenius split if and only if no three lines on it form a "triangle".
Cite
@article{arxiv.2007.12018,
title = {Cubic Surfaces of Characteristic Two},
author = {Zhibek Kadyrsizova and Jennifer Kenkel and Janet Page and Jyoti Singh and Karen E. Smith and Adela Vraciu and Emily E. Witt},
journal= {arXiv preprint arXiv:2007.12018},
year = {2022}
}