The F-splitting ratio of a toric variety

Milena Hering, University of Edinburgh. Part of the Algebra Seminar series.

The Frobenius morphism is a useful tool in the study of commutative rings and algebraic varieties. One of its uses is to give a measurement of how bad the singularities of a ring are. This measurement is called the the F-splitting ratio, which agrees with the F-signature for normal rings. The F-signature of a normal toric ring was computed by Von Korff. I will give give an introduction to these notions and present the computation of the F-splitting ratio of a seminormal toric ring. This is joint work with Kevin Tucker.