Stringy Chern classes of singular toric varieties and their applications
Stringy Chern classes of singular toric varieties and their applications
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奇异环面变种的弦陈氏类及其应用
DOI：
10.4310/cntp.2017.v11.n1.a1
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
K. Schaller
中科院分区：
文献类型：
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作者：
V. Batyrev;K. Schaller
设X是具有最坏对数端点奇点的正规射影Q-Gorenstein变种。我们通过X的全弦陈类证明了X上一般完全交的全弦陈类的一个表达式。这个公式是由它在环变中Calabi-Yau完全交的镜像对称中的应用而得到的。我们计算了任意射影Q-Gorenstein环变的弦型Chern类，并给出了弦型Libgober-Wood恒等式的组合解释。作为应用，我们导出了d维自反多面体与d维数12之间的一个新的组合恒等式。
Let X be a normal projective Q-Gorenstein variety with at worst log-terminal singularities. We prove a formula expressing the total stringy Chern class of a generic complete intersection in X via the total stringy Chern class of X. This formula is motivated by its applications to mirror symmetry for Calabi-Yau complete intersections in toric varieties. We compute stringy Chern classes and give a combinatorial interpretation of the stringy Libgober-Wood identity for arbitrary projective Q-Gorenstein toric varieties. As an application we derive a new combinatorial identity relating d-dimensional reflexive polytopes to the number 12 in dimension d>3.