本征镜像对称和刺破的Gromov-Witten不变量

M. Gross, Bernd S Siebert
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引用次数: 41

摘要

这是2015年AMS暑期代数几何学院(盐湖城)的贡献,宣布了一个一般的镜子结构。这种构造适用于最大边界为D的对数Calabi-Yau对(X,D)或Calabi-Yau流形的最大单幂退化。新的成分是“穿透格罗莫夫-维滕不变量”的概念,目前正在与阿布拉莫维奇和陈一起进行。对(X,D)的镜像构造为使用(X,D)的刺穿不变量定义的环的谱。类似的构造导致了Calabi-Yau流形的镜像。这可以看作是在log CY曲面和K3曲面的情况下,与Hacking和Keel共同开发的结构的推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Intrinsic mirror symmetry and punctured Gromov-Witten invariants
This contribution to the 2015 AMS Summer Institute in Algebraic Geometry (Salt Lake City) announces a general mirror construction. This construction applies to log Calabi-Yau pairs (X,D) with maximal boundary D or to maximally unipotent degenerations of Calabi-Yau manifolds. The new ingredient is a notion of "punctured Gromov-Witten invariant", currently in progress with Abramovich and Chen. The mirror to a pair (X,D) is constructed as the spectrum of a ring defined using the punctured invariants of (X,D). An analogous construction leads to mirrors of Calabi-Yau manifolds. This can be viewed as a generalization of constructions developed jointly with Hacking and Keel in the case of log CY surfaces and K3 surfaces.
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