Singularities of metrics on Hodge bundles and their topological invariants
Journal article, 2018

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.

Log-canonical threshold

Vanishing cycle

Milnor number

Quillen metric

L -metric 2

BCOV metric

Degeneracy index

Hodge bundles

Limit Hodge structure

Author

Dennis Eriksson

Chalmers, Mathematical Sciences, Algebra and geometry

Gerard Freixas I. Montplet

Pierre and Marie Curie University (UPMC)

Christophe Mourougane

University of Rennes 1

Algebraic Geometry

2313-1691 (ISSN) 2214-2584 (eISSN)

Vol. 5 6 742-775

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

DOI

10.14231/AG-2018-021

More information

Latest update

12/7/2018