Classification of extremal hypersurfaces in positive characteristic

Abstract: The log canonical threshold is an invariant that measures how singular a hypersurface over an algebraically closed field of characteristic zero is. The F-pure threshold is the positive characteristic analog. Hypersurfaces with smaller threshold are more singular.

I will discuss a lower bound for a homogeneous polynomial in characteristic p, relative to its degree, and describe the classification of the hypersurfaces that achieve this bound up to change of coordinates. These results were obtained as part of a project started at the A.W.M. Workshop ``Women in Commutative Algebra” at B.I.R.S.; joint work with Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Jyoti Singh, Karen E. Smith and Emily Witt.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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