2003 Fiscal Year Final Research Report Summary
On Pencil genus for normal surface singularities (II)
| Project/Area Number |
14540061
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Gunma University |
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Principal Investigator |
TOMARU Tadashi Gunma University, School of Health Sciences, Professor, 医学部, 教授 (70132579)
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| Co-Investigator(Kenkyū-buntansha) |
OKUMA Tomohiro Gunma National College of Technology, General Education, Associated Professor, 一般教育, 助教授 (00300533)
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| Project Period (FY) |
2002 – 2003
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| Keywords | singularity / families of compact algebraic curve / pencil genus / Kodaira singularity |
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| Research Abstract |
In our research, we have been researching the relation between one parameter families of compact Riemann surfaces (i.e., compact algebraic curves over the complex number field) and normal complex surface singularities. Also we investigated some properties of cyclic coverings of normal surface singularities. Our results are as follows :
1.When the branched divisor is reduced and cyclic order is enoughly higher, we prove that the singularity obtained by cyclic cover is a Kodaira singularity.
2.Three years ago the head investigator (Tomaru) had defined a genus (named "pencil genus") for normal surface singularities. We compute pencil genus for some classes of surface singularities.
3.When we consider singularities obtained by cyclic covering, we observed some phenomena about the change of the forms of exceptional sets of the singularities when we change the cyclic order.
4.We investigated the relation between one parameter families of compact Riemann surfaces with C^*-action and normal surface singularities C^*-action.
5.We investigated the situation of holomorphic differential forms around one parameter families of compact Riemann surfaces.
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