Algebraic Geometry Seminar: Higher multiplier ideals

In this talk, we will discuss the construction of a family of ideal sheaves associated to any Q-divisor on a complex manifold X, indexed by an integer indicating the Hodge level, so that we can view the usual multiplier ideals as the “lowest piece”. Their local and global properties are established using various kinds of D-modules. It is closely related to, but different from, Mustata-Popa’s theory of Hodge ideals. As an application, we give a partial solution of the Riemann-Schottky problem via the singularity of theta divisors on principally polarized abelian varieties. This is based on the joint work in progress with Christian Schnell.