Complex Analytic Geometry

     Speakers

Young-Jun Choi (Pusan National U.)
Yoshinori Hashimoto (Osaka Metropolitan U.)
Dano Kim (Seoul National U.)
Takayuki Koike (Osaka Metropolitan U.)
Seungjae Lee (IBS-CCG)
Nguyen Ngoc Cuong (KAIST)
Mihai Paun (Bayreuth U.)
Martin Sera (Kyoto U. Advanced Science)
Jihun Yum (IBS-CCG)

     Schedule

Oct. 5

      1. Infinitesimal extension of twisted canonical forms and applications (part 1)
        Mihai Paun
        10:30-11:15


      2. Weighted L2 holomorphic functions on ball fiber bundles over compact Kähler manifolds
        Seungjae Lee
        13:30-14:20


      3. Weak solutions to Monge-Ampère type equations on compact Hermitian manifold with boundary
        Nguyen Ngoc Cuong
        14:40-15:30


      4. Limit of Bergman kernels on a tower of coverings of compact Kähler manifolds
        Jihun Yum
        15:50-16:40

Oct. 6

      1. Infinitesimal extension of twisted canonical forms and applications (part 2)
        Mihai Paun
        10:30-11:15


      2. Curvature of higher direct images
        Young-Jun Choi
        13:30-14:20


      3. Some recent results on constant scalar curvature Kähler metrics with cone singularities
        Yoshinori Hashimoto
        14:40-15:30


      4. Projective K3 surfaces which contain Levi-flat hypersurfaces
        Takayuki Koike
        15:50-16:40

Oct. 7

      1. Hermite-Einstein metrics on stable reflexive sheaves on Kaehler manifolds
        Mihai Paun
        10:30-11:15


      2. Lelong numbers of direct images of generalized Monge-Ampère products
        Martin Sera
        13:30-14:20


      3. Canonical bundle formula and degenerating families of volume forms
        Dano Kim
        14:40-15:30

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.

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