BCOV invariants of Calabi--Yau manifolds and degenerations of Hodge structures.

Content Provider	Semantic Scholar
Author	Eriksson, Dennis Montplet, Gérard Freixas I. Mourougane, Christophe
Copyright Year	2018
Abstract	Calabi-Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky-Cecotti-Ooguri-Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi-Yau manifold is related to a conjectured invariant, only depending on the complex structure of the mirror, and built from Ray-Singer holomorphic analytic torsions. To this end, extending work of Fang-Lu-Yoshikawa in dimension 3, we introduce and study the BCOV invariant of Calabi-Yau manifolds of arbitrary dimension. To determine it, knowledge of its behaviour at the boundary of moduli spaces is imperative. We address this problem by proving precise asymptotics along one-parameter degenerations, in terms of topological data and intersection theory. Central to the approach are new results on degenerations of $L^2$ metrics on Hodge bundles, combined with information on the singularities of Quillen metrics in our previous work.
File Format	PDF HTM / HTML
Alternate Webpage(s)	https://arxiv.org/pdf/1809.05452v1.pdf
Alternate Webpage(s)	https://webusers.imj-prg.fr/~gerard.freixas/Preprints/eriksson-freixas-mourougane-BCOV.pdf
Alternate Webpage(s)	https://perso.univ-rennes1.fr/christophe.mourougane/recherche/metric/BCOV-invariant.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article