## Dano Kim, Canonical Bundle Formula and Degenerating Families of Volume Forms

### Speaker

Dano Kim
Department of Mathematical Sciences, Seoul National University

We will talk about a metric version of Kawamata’s canonical bundle formula for log Calabi-Yau fibrations: the L2 metric carries singularity described by the discriminant divisor and the moduli part line bundle has a singular hermitian metric with vanishing Lelong numbers. This answers a folklore conjecture arising from work of Kawamata and Tsuji and a question of Eriksson, Freixas i Montplet and Mourougane. It has immediate applications to L2 extension theorems which was our starting point.