Gauss–Manin Connection in Disguise: Calabi–Yau Threefolds
Gauss–Manin Connection in Disguise: Calabi–Yau Threefolds
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DOI：
10.1007/s00220-016-2640-9
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发表时间：
2014-10
影响因子：
2.4
通讯作者：
M. Alim;H. Movasati;E. Scheidegger;S. Yau
中科院分区：
文献类型：
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作者：
M. Alim;H. Movasati;E. Scheidegger;S. Yau
本文描述了非刚性紧Calabi-Yau三重微分形式增强模空间上的李代数及其与Bershadsky-Cecotti-Ooguri-Vafa全纯反常方程的关系.特别是，我们描述了代数拓扑弦配分函数，它编码的多项式结构的全纯和非全纯拓扑弦配分函数。我们的方法是基于Grothendieck的代数de Rham上同调和代数Gauss-Manin连接。这样，我们恢复了Yamaguchi-Yau和Alim-Länge在代数上下文中的一个结果。我们的证明使用的特殊多项式生成元定义的特殊几何的变形空间的Calabi-Yau三倍对应于这样的模空间上的坐标。我们以镜像五次曲线为例进行讨论。
We describe a Lie Algebra on the moduli space of non-rigid compact Calabi–Yau threefolds enhanced with differential forms and its relation to the Bershadsky–Cecotti–Ooguri–Vafa holomorphic anomaly equation. In particular, we describe algebraic topological string partition functions, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck’s algebraic de Rham cohomology and on the algebraic Gauss–Manin connection. In this way, we recover a result of Yamaguchi–Yau and Alim–Länge in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi–Yau threefolds correspond to coordinates on such a moduli space. We discuss the mirror quintic as an example.