A subadditivity property of multiplier ideals.

Abstract

Let X be a smooth complex quasi-projective variety, and let D be an effective Q-divisor on X. One can associate to D its multiplier ideal sheaf J (D) = J (X,D) ⊆ OX , whose zeroes are supported on the locus at which the pair (X,D) fails to have log-terminal singularities. It is useful to think of J (D) as reflecting in a somewhat subtle way the singularities of D: the “worse” the singularities, the smaller the ideal. These ideals and their variants have come to play an increasingly important role in higher dimensional geometry, largely because of their strong vanishing properties. Among the papers in which they figure prominently, we might mention for instance [30], [4], [33], [2], [13], [34], [19], [14] and [8]. See [6] for a survey.