Special Colloquium
Kevin Tucker
Princeton University
An Introduction to F-signature
Abstract: While most points on an algebraic variety are smooth, understanding the singular or non-manifold points
of an algebraic variety is an essential part of many investigations. In prime characteristic p > 0,
the Frobenius endomorphism or p-th power map can be used to detect and characterize singularities.
To that end, the F-signature is a local numerical invariant defined via Frobenius and is thought to
capture subtle arithmetic and geometric information. Unfortunately, like many so-called F-invariants,
explicit computations of F-signature are often extremely difficult and a complete understanding of
its meaning remains elusive. In this talk, we will give an introduction to the circle of ideas surrounding
F-signature together with a number of examples and conjectures. Time permitting, we will also briefly
talk about the relationship between F-signature and the singularities appearing in
complex birational algebraic geometry.
Tea at 4:15
Friday December 7, 2012 at 3:00 PM in SEO 636