Singularities of metrics on Hodge bundles and their topological invariants
Abstract
We consider degenerations of complex projective Calabi--Yau 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 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.
- Publication:
-
arXiv e-prints
- 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)
- E-Print:
- Algebraic Geometry 5 (6) (2018) 742-775