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Singularities of metrics on Hodge bundles and their topological invariants

Journal article
Authors Dennis Eriksson
G. F. I. Montplet
C. Mourougane
Published in Algebraic Geometry
Volume 5
Issue 6
Pages 742-775
ISSN 2313-1691
Publication year 2018
Published at Department of Mathematical Sciences
Pages 742-775
Language en
Links dx.doi.org/10.14231/AG-2018-021
Keywords BCOV metric, Degeneracy index, Hodge bundles, L2-metric, Limit Hodge structure, Log-canonical threshold, Milnor number, Quillen metric, Vanishing cycle
Subject categories Algebra and geometry

Abstract

We consider degenerations of complex projective Calabi-Yau varieties and study the singularities of L2, 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. © Foundation Compositio Mathematica 2018.

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