Karen E. Smith (University of Michigan)Title: Values of the F-pure threshold for homogeneous polynomialsAbstract: Fix a field k of prime characteristic p. The set of all homogeneous degree d polynomials in n variables (up to scalar multiple) naturally forms a projective space of dimension n-1 over k. This projective space admits a stratification by locally closed subsets consisting of polynomials with the same F-pure threshold. I will discuss a formula, in terms of n, d, and p, for the value of the F-pure threshold of the generic polynomial of degree d in n variables over k. For polynomials in two variables, we can say more about the values of the F-pure threshold for each stratum--they are always a (specific) truncation of the base p expansion of the generic F-pure threshold. This work is joint with Adela Vraciu, and closely related to work of Hernandez, Núñez-Betancourt, Witt and Zhang. In fact, we provide an example to resolve, negatively, a question proposed by those authors, as well as evidence supporting and refining their ideas.
- Tags
-