## Seminar on Geometric Complex Analysis

Date, time & place Monday 10:30 - 12:00 Room #128 (Graduate School of Math. Sci. Bldg.) Kengo Hirachi, Shigeharu Takayama, Ryosuke Nomura

Next seminar

### 2017/09/25

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Christophe Mourougane (Université Rennes 1)
Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties
[ Abstract ]
It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet.
Our first motivation is to give a metric analogue of Kodaira's canonical bundle formula for elliptic surfaces, in the case of families of Calabi-Yau varieties. We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of $L^2$, Quillen and BCOV metrics on Hodge and determinant bundles. The dominant and subdominant terms in the expansions of the metrics close to non-smooth fibres are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds.