Singularities of metrics on Hodge bundles and their topological invariants
Artikel i vetenskaplig tidskrift, 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

Författare

Dennis Eriksson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Gerard Freixas I. Montplet

Université Pierre et Marie Curie (UPMC)

Christophe Mourougane

Université de Rennes 1

Algebraic Geometry

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

Vol. 5 6 742-775

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.14231/AG-2018-021

Mer information

Senast uppdaterat

2018-12-07