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arXiv · 1611.03017

Singularities of metrics on Hodge bundles and their topological invariants

Dennis Eriksson·Gerard Freixas i Montplet·Christophe Mourougane
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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.

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Dennis Eriksson, Gerard Freixas i Montplet, Christophe Mourougane. 2016-11-09. Singularities of metrics on Hodge bundles and their topological invariants. https://doi.org/10.14231/ag-2018-021

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