Classification of Frobenius Forms in five variables

Abstract

We classify Frobenius forms, a special class of homogeneous polynomials in characteristic $p>0$, in up to five variables over an algebraically closed field. We also point out some of the similarities with quadratic forms.

Appears in Springer volume "Women in Commutative Algebra--Proceedings of the 2019 WICA Workshop". Note that in "Lower Bounds on the F-pure Threshold and Extremal Singularities" (with Jennifer Kenkel, arxiv:2009.13679 [v3], to appear in Transactions of the AMS), we completely classify all extremal singularities of fixed degree and embedding dimension up to projective equivalence