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".
| Original language | English |
|---|---|
| Pages (from-to) | 6251-6267 |
| Number of pages | 17 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 374 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2021 |
Funding
This project was partially supported by the National Science Foundation (grant number 1934391), the Banff International Research Station (workshop 19w5104), and the Association for Women in Mathematics (grant number NSF-HRD 1500481). This paper began at a weeklong research workshop called Women in Commutative Algebra at the Banff International Research Station in October 2019 and partially funded by US NSF and the AWM. In addition, the fourth author was partially supported by SERB(DST) grant number ECR/2017/000963, the fifth author was partially supported by NSF grant numbers 1801697, 1952399, and 2101075 and the seventh author was partially supported by NSF CAREER grant 1945611.
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics
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