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arXiv · 2007.12018

Cubic Surfaces of Characteristic Two

Zhibek Kadyrsizova·Jennifer Kenkel·Janet Page·Jyoti Singh·Karen E. Smith·Adela Vraciu·Emily E. Witt
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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".

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Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith, Adela Vraciu, Emily E. Witt. 2020-07-23. Cubic Surfaces of Characteristic Two. https://doi.org/10.1090/tran/8341

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