21 octobre 2019

Eleonora Di Nezza (IMJ-PRG)
Metric geometry of singularity types

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Lieu : IMO, salle 3L8.

Résumé : (Quasi)-Plurisubharmonic functions are a key notion in complex geometry. The study of their singularity (in terms -for example- of integrability properties or smoothing procedures) is conceived to develop analytic techniques in order to solve problems in complex and algebraic geometry.
In this talk we study the space of all possible singularity types of quasi-plurisubharmonic functions and we introduce a natural (pseudo)-distance on it.
As applications we present a stability result for complex Monge-Ampère equations with prescribed singularity and a semicontinuity result for multiplier ideal sheaves associated to singularity types. This is a joint work with T. Darvas and C. Lu.

Metric geometry of singularity types  Version PDF