BCOV invariants of Calabi--Yau manifolds and degenerations of Hodge structures
| Autor: | Eriksson, Dennis, Montplet, Gerard Freixas i, Mourougane, Christophe |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Duke Math. J. 170, no. 3 (2021), 379-454 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1215/00127094-2020-0045 |
| Popis: | 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. Comment: Minor revision. Mainly restructure of the text, minor improvements and corrections. Added information about subdominant terms of $L^2$-norms |
| Databáze: | arXiv |
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