Stringy Hodge numbers of varieties with Gorenstein canonical singularities
Stringy Hodge numbers of varieties with Gorenstein canonical singularities
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具有 Gorenstein 规范奇点的簇的弦霍奇数
DOI：
10.1016/j.jalgebra.2003.12.015
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
V. Batyrev
中科院分区：
文献类型：
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作者：
V. Batyrev
本文对任意正规不可约代数簇X引入了弦E-函数的概念，该代数簇X在最坏情况下具有对数终端奇点。证明了弦E-函数的一些基本性质，并对任意的Q-Gorenstein复曲面簇进行了显式计算。利用弦E-函数，我们提出了一个一般的方法来定义弦霍奇数的投射代数簇在最坏的Gorenstein典型奇点。这使我们能够制定具有典范奇异性的任意卡-丘簇的拓扑镜像对偶检验。在附录中，我们解释了弧空间上的非阿基米德积分。我们需要这些积分来证明弦霍奇数定义中使用的主要技术陈述。
We introduce the notion of stringy E-function for an arbitrary normal irreducible algebraic variety X with at worst log-terminal singularities. We prove some basic properties of stringy E-functions and compute them explicitly for arbitrary Q-Gorenstein toric varieties. Using stringy E-functions, we propose a general method to define stringy Hodge numbers for projective algebraic varieties with at worst Gorenstein canonical singularities. This allows us to formulate the topological mirror duality test for arbitrary Calabi-Yau varieties with canonical singularities. In Appendix we explain non-Archimedian integrals over spaces of arcs. We need these integrals for the proof of the main technical statement used in the definition of stringy Hodge numbers.