The F-signature function of a globally F-regular variety.

Abstract: Strongly F-regular local rings are an important class of mild
singularities in positive characteristics, analogous to Kawamata log
terminal (klt) singularities. The F-signature of a strongly F-regular local
ring R is an interesting invariant of its singularities. In this talk, we
will discuss this invariant when R is the section ring of a projective
variety with respect to an ample divisor. In particular, we study how the
F-signature varies as we vary the ample divisor. For this purpose, we will
introduce the F-signature function, a real valued function on the ample
cone of X, and discuss its continuity properties. This function is
analogous to the well-known volume function of big divisors. This is joint
work with Seungsu Lee.