Cubic surfaces of characteristic two
Kadyrsizova Z. Kenkel J. Page J. Singh J. Smith K.E. Vraciu A. Witt E.E.
2021American Mathematical Society
Transactions of the American Mathematical Society
2021#374Issue 96251 - 6267 pp.
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.
Text of the article Перейти на текст статьи
Nazarbayev University, Nur-Sultan, Kazakhstan
Department of Mathematics, University of Michigan, Ann Arbor, MI, United States
Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, India
Department of Mathematics, University of South Carolina, Columbia, SC, United States
Department of Mathematics, University of Kansas, Lawrence, KS, United States
Nazarbayev University
Department of Mathematics
Department of Mathematics
Department of Mathematics
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026