1999 Fiscal Year Final Research Report Summary

Research of Quasi-Kodaira singularities

Research Project

Project/Area Number	10640062
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Geometry
Research Institution	Gunma University
Principal Investigator	TOMARU Tadashi Faculty of Medicine, Gunma University Professor, 医学部, 教授 (70132579)
Co-Investigator(Kenkyū-buntansha)	OKUMA Tomohiro Gunma Institute of Technology, lecturer, 一般教科, 講師 (00300533)
Project Period (FY)	1998 – 1999
Keywords	singularity / degeneration / curve / pencil genus / geometric genus
Research Abstract	In this research, we have investigated the relation between degeneration of algeraic curves and normal surface singularities. First we gave the definiton of quasi-Kodaira singularities and gave some sufficient conditions for normal surface singularities to be quasi-Kodaira. Second we considered hypersuface normal surface singularities (namely, the equation is z^n=f(x,Y) ). For the class, we found an interesting class of quasi-Kodaira singularities. Third, we prove an interesting result about cyclic covers of normal surface singularities. Under some conditions, if the order of the group of the cyclic cover is sufficiently large, then the cyclic cover over a normal surface singularity is a quasi-Kodaira singularity. Fourth, we prove some formulae about geometric genus of elliptic quasi-Kodaira singularity.

(4 results)