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摘要翻译：
根据Sen的F-理论的弱耦合极限作为IIB类型的鉴别，蝌蚪条件的相容性导致了一个关于椭圆纤维卡拉比-尤四重曲面和某些相关曲面的欧拉特性的非平凡恒等式。在考虑到相关轨迹的奇点之后，我们给出了导致恒等式的物理论证，以及证实它的Chern类恒等式的数学推导。Chern类的这种同一性在任意维度中成立，对于不一定是卡拉比-尤的变种也成立。奇点在物理和数学论证中都是必不可少的：蝌蚪关系可以被解释为一个恒等式，涉及奇异超曲面的弦不变量和对夹点存在的修正。利用奇异变体的Chern-Schwartz-MacPherson类简化了数学讨论。我们还说明了如何通过对适当的可构造函数应用“Verdier专门化”来获得主恒等式。
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英文标题：
《Chern class identities from tadpole matching in type IIB and F-theory》
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作者：
Paolo Aluffi (FSU), Mboyo Esole (KU Leuven)
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：High Energy Physics - Theory 高能物理-理论
分类描述：Formal aspects of quantum field theory. String theory, supersymmetry and supergravity.
量子场论的形式方面。弦理论，超对称性和超引力。
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In light of Sen's weak coupling limit of F-theory as a type IIB orientifold, the compatibility of the tadpole conditions leads to a non-trivial identity relating the Euler characteristics of an elliptically fibered Calabi-Yau fourfold and of certain related surfaces. We present the physical argument leading to the identity, and a mathematical derivation of a Chern class identity which confirms it, after taking into account singularities of the relevant loci. This identity of Chern classes holds in arbitrary dimension, and for varieties that are not necessarily Calabi-Yau. Singularities are essential in both the physics and the mathematics arguments: the tadpole relation may be interpreted as an identity involving stringy invariants of a singular hypersurface, and corrections for the presence of pinch-points. The mathematical discussion is streamlined by the use of Chern-Schwartz-MacPherson classes of singular varieties. We also show how the main identity may be obtained by applying `Verdier specialization' to suitable constructible functions.
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PDF链接：
https://arxiv.org/pdf/0710.2544
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