The jumping coefficients of non-Q-Gorenstein multiplier ideals

Topology of Algebraic Varieties
Topic:The jumping coefficients of non-Q-Gorenstein multiplier ideals
Speaker:Patrick Graf
Affiliation:Universit├Ąt Bayreuth
Date:Wednesday, March 4
Time/Room:11:15am - 12:15pm/S-101
Video Link:http://video.ias.edu/tav/2015/0304-PatrickGraf

De Fernex and Hacon associated a multiplier ideal sheaf to a pair $(X, \mathfrak a^c)$ consisting of a normal variety and a closed subscheme, which generalizes the usual notion where the canonical divisor $K_X$ is assumed to be Q-Cartier. I will discuss a recent work of mine on the jumping numbers associated to these multiplier ideals. The set of jumping numbers of a pair is unbounded, countable and satisfies a certain periodicity property. Furthermore, the jumping numbers form a discrete set of real numbers if the locus where $K_X$ fails to be Q-Cartier is zero-dimensional. In particular, discreteness holds whenever $X$ is a threefold with rational singularities.