JUMPING NUMBERS ON ALGEBRAIC SURFACES
KEVIN TUCKER, University of Michigan

Abstract. Jumping numbers are local invariants of an ideal sheaf on a complex algebraic variety. These invariants are known to encode various algebraic and geometric data about the associated closed subscheme. However, their computation requires a resolution of singularities and is problematic in general. We will introduce these invariants along with multiplier ideals, and talk about methods for computing jumping numbers on surfaces. In particular, we will mention recent advances in finding and understanding the jumping numbers of a plane curve.