Methods and Applications of Analysis

Volume 26 (2019)

Number 1

In Memory of Professor John N. Mather: Part 3 of 3

Guest Editors: Sen Hu, University of Science and Technology, China; Stanisław Janeczko, Polish Academy of Sciences, Poland; Stephen S.-T. Yau, Tsinghua University, China; and Huaiqing Zuo, Tsinghua University, China.

On the Newton polyhedrons with one inner lattice point

Pages: 1 – 12

DOI: https://dx.doi.org/10.4310/MAA.2019.v26.n1.a1

Authors

Xue Luo (School of Mathematical Sciences, Beihang University, Beijing, China)

Fang Wang (School of Mathematical Sciences, Beihang University, Beijing, China)

Abstract

Geometric genus is an important invariant in the classification theory for isolated singularities. In this paper we give a complete classification of three-dimensional isolated weighted homogeneous singularities with geometric genus one. This is one of important classes of minimally elliptic singularities. We reduce it to nineteen classes Newton polyhedrons with one inner lattice point.

Keywords

geometric genus, isolated singularity

2010 Mathematics Subject Classification

32S05

Full Text (PDF format)

This work is financially supported by the National Natural Science Foundation of China (grant no. 11871003) and by the Fundamental Research Funds for the Central Universities (YWF-19-BJ-J-269).

Received 25 April 2018

Accepted 6 August 2018

Published 14 November 2019