Piotr Achinger

Title: F-splitting and F-regularity of varieties with a diagonalizable group action

Abstract: 
We will investigate the F-splitting and F-regularity properties of normal
varieties in positive characteristic equipped with an effective torus (or more
generally diagonalizable group scheme) action. The main result relates
invariant F-splittings of such a variety to F-splittings of a suitable
quotient log pair. We apply this to study varieties with complexity one torus
action, cyclic covers, toric vector bundles, and diagonal splittings. This is
joint work with Nathan Ilten and Hendrik Suess.