与Koszul矩阵分解相关的上同调类的齐性
Homogeneity of cohomology classes associated with Koszul matrix factorizations
摘要：
在这项工作中，我们证明了所谓的维数属性的上同调域论与齐次多项式W的孤立奇点，在代数框架arXiv：1105.2903。这相当于表明，一些上同调类的Deligne-Mumford模空间的稳定曲线，构造使用傅立叶-Mukai型函子与矩阵分解，生活在规定的维度。该证明基于arXiv：math/0011032中建立的同质性结果，用于0的Koszul矩阵分解的某些特征类。为了减少到这个结果，我们使用的理论，傅立叶-Mukai型函子涉及矩阵分解和自然的合理格在相关的霍赫希尔德同调空间，以及一个版本的Hodge-Riemann双线性关系的霍赫希尔德同调的矩阵分解。我们的方法还证明了某些具有孤立奇点的拟齐次多项式的上同调域论的维数性质。
英文摘要：
In this work we prove the so called dimension property for the cohomological field theory associated with a homogeneous polynomial W with an isolated singularity, in the algebraic framework of arXiv:1105.2903. This amounts to showing that some cohomology classes on the Deligne-Mumford moduli spaces of stable curves, constructed using Fourier-Mukai type functors associated with matrix factorizations, live in prescribed dimension. The proof is based on a homogeneity result established in arXiv:math/0011032 for certain characteristic classes of Koszul matrix factorizations of 0. To reduce to this result we use the theory of Fourier-Mukai type functors involving matrix factorizations and the natural rational lattices in the relevant Hochschild homology spaces, as well as a version of Hodge-Riemann bilinear relations for Hochschild homology of matrix factorizations. Our approach also gives a proof of the dimension property for the cohomological field theories associated with some quasihomogeneous polynomials with an isolated singularity.
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