论文标题
BCOV不变性的动机融合和异性不变性
Motivic integration and the birational invariance of BCOV invariants
论文作者
论文摘要
Bershadsky，Cecotti，Ooguri和Vafa为Calabi-Yau歧管构建了一个现实价值的不变性，现在称为BCOV TORSION。基于它，一个独立于公制的不变性，称为BCOV不变性，由Fang-lu-yoshikawa和Eriksson-Freixas I Montplet-Mourougane构建。 BCOV不变性通过镜像对称性与Gromov的理论相关。基于第二作者的先前工作，我们证明了Birational Calabi-Yau流形具有相同的BCOV不变性的猜想。我们还将BCOV不变性的构造扩展到具有川田对数末端奇异性的Calabi-Yau品种，并证明了其对Calabi的生育不变性 - 具有典型的奇异性的Yau品种。我们使用动机融合理论对我们的构建进行解释。
Bershadsky, Cecotti, Ooguri, and Vafa constructed a real-valued invariant for Calabi--Yau manifolds, which is now called the BCOV torsion. Based on it, a metric-independent invariant, called the BCOV invariant, was constructed by Fang--Lu--Yoshikawa and Eriksson--Freixas i Montplet--Mourougane. The BCOV invariant is conjecturally related to the Gromov--Witten theory via mirror symmetry. Based upon the previous work of the second author, we prove the conjecture that birational Calabi--Yau manifolds have the same BCOV invariant. We also extend the construction of the BCOV invariant to Calabi--Yau varieties with Kawamata log terminal singularities and prove its birational invariance for Calabi--Yau varieties with canonical singularities. We provide an interpretation of our construction using the theory of motivic integration.
