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| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
2017年09月25日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
Christophe Mourougane 氏 (Université de Rennes 1)
Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties
Christophe Mourougane 氏 (Université de Rennes 1)
Asymptotics of $L^2$ and Quillen metrics in degenerations of Calabi-Yau varieties
[ 講演概要 ]
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.
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.
