Singularities of metrics on Hodge bundles and their topological invariants
Abstract
We consider degenerations of complex projective CalabiYau 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 nonsmooth fibers are shown to be related to wellknown topological invariants of singularities, such as limit Hodge structures, vanishing cycles and logcanonical thresholds. We also describe corresponding invariants for more general degenerating families in the case of the Quillen metric.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 DOI:
 10.48550/arXiv.1611.03017
 arXiv:
 arXiv:1611.03017
 Bibcode:
 2016arXiv161103017E
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables;
 Mathematics  Differential Geometry;
 14J32;
 58K55;
 58J52 (Primary);
 58K65;
 14J70 (Secondary)
 EPrint:
 Algebraic Geometry 5 (6) (2018) 742775