Methods and Applications of Analysis

Volume 24 (2017)

Number 2

Special issue dedicated to Henry B. Laufer on the occasion of his 70th birthday: Part 2

Guest Editors: Stephen S.-T. Yau (Tsinghua University, China); Gert-Martin Greuel (University of Kaiserslautern, Germany); Jonathan Wahl (University of North Carolina, USA); Rong Du (East China Normal University, China); Yun Gao (Shanghai Jiao Tong University, China); and Huaiqing Zuo (Tsinghua University, China)

Analytic singularities supported by a specific integral homology sphere link

Pages: 303 – 320

DOI: https://dx.doi.org/10.4310/MAA.2017.v24.n2.a7

Authors

András Némethi (Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary; ELTE, University of Budapest, Hungary; and the Basque Center for Applied Mathematics, Bilbao, Spain)

Tomohiro Okuma (Department of Mathematical Sciences, Faculty of Science, Yamagata University, Yamagata, Japan)

Abstract

The main question we target is the following: If one fixes a topological type (of a complex normal surface singularity) then what are the possible analytic types supported by it, and/or, what are the possible values of the geometric genus? We answer the question for a specific (in some sense pathological) topological type, which supports rather different analytic structures. These structures are listed together with some of their key analytic invariants.

Keywords

surface singularity, integral homology sphere, geometric genus, multiplicity, analytic types, Kodaira singularities, splice singularities

2010 Mathematics Subject Classification

Primary 32S25. Secondary 14B05, 14J17.

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The first author was partially supported by NKFIH Grant 112735 and ERC Adv. Grant LDTBud of A. Stipsicz at Rényi Institute of Math., Budapest

The second author was partially supported by JSPS KAKENHI Grant Number 26400064.

Received 7 November 2016

Accepted 15 February 2017

Published 3 January 2018