Year: 2021
Type: article
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”.
DOI: 10.1090/tran/8341
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Commutative Algebra: Extremal Singularities in Prime Characteristic, G1213652881, Commutative Algebra: F-Regularity in Algebraic Geometry and Non-Commutative Algebra, G1627848978, FRG: Collaborative Research: Algebraic Geometry and Singularities in Positive and Mixed Characteristic, G3936155006, G4724987711, CAREER: New Frontiers for Frobenius, Singularity Theory, Differential Operators, and Local Cohomology, G5844624468, G8909120457
OpenAlex ID: W3045339557