Methods and Applications of Analysis

Volume 24 (2017)

Number 1

Special issue dedicated to Henry B. Laufer on the occasion of his 70th birthday: Part 1

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)

Certain normal surface singularities of general type

Pages: 71 – 97



Kazuhiro Konno (Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, Japan)


Koyama’s inequality for normal surface singularities gives the upper bound on the self-intersection number of the canonical cycle in terms of the arithmetic genus. For those singularities of fundamental genus two attaining the bound, a formula for computing the geometric genus is shown and the resolution dual graphs are roughly classified. In Gorenstein case, the multiplicity and the embedding dimension are also computed.


even singularity, canonical cycle, Yau cycle, maximal ideal cycle

2010 Mathematics Subject Classification

14B05, 14J17

Partly supported by Grants-in-Aid for Scientific Research (A) (No. 24244002) by Japan Society for the Promotion of Science (JSPS).

Received 31 January 2016

Published 18 August 2017