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A sharp lower bound for the geometric genus and Zariski multiplicity question

Stephen Yau Tsinghua University Huaiqing Zuo Tsinghua University

mathscidoc:1803.01005

Math Z., 2017.12
It is well known that the geometric genus andmultiplicity are two important invariants for isolated singularities. In this paper we give a sharp lower estimate of the geometric genus in terms of the multiplicity for isolated hypersurface singularities. In 1971, Zariski asked whether the multiplicity of an isolated hypersurface singularity depends only on its embedded topological type. This problem remains unsettled. In this paper we answer positively Zariski’s multiplicity question for isolated hypersurface singularity if Milnor number or geometric genus is small.
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@inproceedings{stephen2017a,
  title={A sharp lower bound for the geometric genus and Zariski multiplicity question},
  author={Stephen Yau, and Huaiqing Zuo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180307151031060682976},
  booktitle={Math Z.},
  year={2017},
}
Stephen Yau, and Huaiqing Zuo. A sharp lower bound for the geometric genus and Zariski multiplicity question. 2017. In Math Z.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180307151031060682976.
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