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

作者：Yau, Stephen S. -T.^*; Zuo, Huaiqing

来源：Mathematische Zeitschrift, 2018, 289(3-4): 1299-1310.

DOI：10.1007/s00209-017-1999-4

• Geometric genus
• Multiplicity
• Isolated singularity

It is well known that the geometric genus and multiplicity 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.

• 出版日期2018-8
• 单位清华大学