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NCTS Seminar on Algebraic Geometry
10:30 - 11:20, June 21, 2017 (Wednesday)
Room 440, Astronomy-Mathematics Building, NTU
(台灣大學天文數學館 440室)
A Sharp Lower Bound for the Geometric Genus and Zariski Multiplicity Question
Stephen S. T. Yau (Tsinghua University & University of Illinois at Chicago)


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. This is a joint work with Huaiqing Zuo.


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