非单纯环带Landau--Ginzburg数据的弦论不规则Hodge数

中文摘要 AI 辅助

我们将轨道折叠不规则Hodge理论从单纯环带Landau--Ginzburg模型扩展到由可能非单纯的堆栈扇定义的数据。对于Clarke镜像对，我们在环带面环上构造了一个滤过的Koszul--de Rham复形。对于单纯射线支撑数据，一个严格的滤过比较将该复形与Harder--Lee胞腔留数复形等同起来，因此它计算轨道折叠不规则Hodge数。利用该复形，对于固定的可能非单纯数据，我们证明了当其势在无穷远处非退化时，由其射影crepant单纯细分得到的模型具有相同的轨道折叠不规则Hodge多项式。这个共同值定义了原始数据的弦论不规则Hodge数。

英文摘要

We extend orbifold irregular Hodge theory from simplicial toric Landau--Ginzburg models to data defined by possibly non-simplicial stacky fans. For a Clarke mirror pair, we construct a filtered Koszul--de Rham complex over toric face rings. For simplicial ray-supported data, a strict filtered comparison identifies this complex with the Harder--Lee cellular residue complex, and hence it computes the orbifold irregular Hodge numbers. Using this complex, for a fixed possibly non-simplicial datum, we prove that the models obtained from its projective crepant simplicial subdivisions have the same orbifold irregular Hodge polynomial whenever the potential is nondegenerate at infinity. This common value defines the stringy irregular Hodge numbers of the original datum.

发表机构

• Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）

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