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 6 742-775Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.14231/AG-2018-021