31 oct 2017 -- 16:00
Aula D'Antoni, Dip.Matematica, Università "Tor Vergata", Roma
Abstract.
It is a joint work with Dennis Eriksson and Gerard Freixas i Montplet. Our first motivation is to give a metric analogue of Kodaira's canonical bundle formula for elliptic surfaces, in the case of families of Calabi-Yau varieties. 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 fibres are shown to be related to well-known topological invariants of singularities, such as limit Hodge structures, vanishing cycles and log-canonical thresholds.