Singularities of metrics on Hodge bundles and their topological invariants

Eriksson, Dennis; Freixas i Montplet, Gerard; Mourougane, Christophe

doi:10.14231/AG-2018-021

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Singularities of metrics on Hodge bundles and their topological invariants

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Eriksson, Dennis
Max Planck Institute for Mathematics, Max Planck Society;

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Eriksson, D., Freixas i Montplet, G., & Mourougane, C. (2018). Singularities of metrics on Hodge bundles and their topological invariants. Algebraic Geometry, 5(6), 742-775. doi:10.14231/AG-2018-021.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6748-8

Abstract

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 fibers are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds. We also describe corresponding invariants for more general degenerating families in the case of the Quillen metric.