Differential zeros of certain special functions

Jingyue Chen An Huang Bong H Lian Shing-Tung Yau

Algebraic Geometry mathscidoc:1912.43690

arXiv preprint arXiv:1709.00713
In this paper, we study the zero loci of local systems of the form \delta\Pi , where \delta\Pi is the period sheaf of the universal family of CY hypersurfaces in a suitable ambient space \delta\Pi , and \delta\Pi is a given differential operator on the space of sections \delta\Pi . Using earlier results of three of the authors and their collaborators, we give several different descriptions of the zero locus of \delta\Pi . As applications, we prove that the locus is algebraic and in some cases, non-empty. We also give an explicit way to compute the polynomial defining equations of the locus in some cases. This description gives rise to a natural stratification to the zero locus.
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  title={Differential zeros of certain special functions},
  author={Jingyue Chen, An Huang, Bong H Lian, and Shing-Tung Yau},
  booktitle={arXiv preprint arXiv:1709.00713},
Jingyue Chen, An Huang, Bong H Lian, and Shing-Tung Yau. Differential zeros of certain special functions. In arXiv preprint arXiv:1709.00713. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205016903359254.
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