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- Title
A sharp lower bound for the geometric genus and Zariski multiplicity question.
- Authors
Yau, Stephen S.-T.; Zuo, Huaiqing
- Abstract
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.
- Publication
Mathematische Zeitschrift, 2018, Vol 289, Issue 3/4, p1299
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-017-1999-4