Research of QuasiKodaira singularities
Project/Area Number  10640062 
Research Category 
GrantinAid for Scientific Research (C).

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)

CoInvestigator(Kenkyūbuntansha) 
OKUMA Tomohiro Gunma Institute of Technology, lecturer, 一般教科, 講師 (00300533)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1999 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)

Keywords  singularity / degeneration / curve / pencil genus / geometric genus / 特異点 / 曲線の退化 / Pencil種数 / 幾何種数 / quasiKodaira特異点 / 代数曲線の退化族 / 基本サイクル / 有限巡回被覆 / 基本種数 
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 quasiKodaira singularities and gave some sufficient conditions for normal surface singularities to be quasiKodaira. 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 quasiKodaira 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 quasiKodaira singularity. Fourth, we prove some formulae about geometric genus of elliptic quasiKodaira singularity.

Report
(4results)
Research Output
(12results)