Cubic Surfaces of Characteristic Two
Document 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”.
Digital Object Identifier (DOI)
Publication Info
Published in American Mathematical Society, Volume 374, Issue 9, 2021, pages 6251-6267.
APA Citation
Kadyrsizova, Z., Kenkel, J., Page, J., Singh, J., Smith, K., Vraciu, A., & Witt, E. (2021). Cubic surfaces of characteristic two. Transactions of the American Mathematical Society, 374(9), 6251–6267. https://doi.org/10.1090/tran/8341