BCOV invariants of Calabi-Yau manifolds and degenerations of Hodge structures
Artikel i vetenskaplig tidskrift, 2021

Calabi-Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky, Cecotti, Ooguri, and 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, and Yoshikawa in dimension 3, we introduce and study the BCOV invariant of Calabi-Yau manifolds of arbitrary dimension. To determine it, knowledge of its behavior at the boundary of moduli spaces is imperative. To address this problem, we prove general results on degenerations of L-2-metrics on Hodge bundles and their determinants, refining the work of Schmid. We express the singularities of these metrics in terms of limiting Hodge structures and derive consequences for the dominant and subdominant singular terms of the BCOV invariant.


Dennis Eriksson

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

Gerard Freixas I. Montplet

Institut de mathématiques de Jussieu – Paris Rive Gauche

Christophe Mourougane

Institut de recherche mathématique de Rennes

Duke Mathematical Journal

0012-7094 (ISSN)

Vol. 170 3 379-454


Algebra och logik


Matematisk analys



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