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2003 Fiscal Year Final Research Report Summary

On Pencil genus for normal surface singularities (II)

Research Project

Project/Area Number 14540061
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionGunma University

Principal Investigator

TOMARU Tadashi  Gunma University, School of Health Sciences, Professor, 医学部, 教授 (70132579)

Co-Investigator(Kenkyū-buntansha) OKUMA Tomohiro  Gunma National College of Technology, General Education, Associated Professor, 一般教育, 助教授 (00300533)
Project Period (FY) 2002 – 2003
Keywordssingularity / families of compact algebraic curve / pencil genus / Kodaira singularity
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.

  • Research Products

    (4 results)

All Other

All Publications (4 results)

  • [Publications] 都丸 正: "On some classes of weakly Kodaira singularities"Proceedings of the Franco-Japanese Luminy Conference of singularities. (Societe Mathmatique de France). (掲載受理).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 奥間 智弘: "On ($-P\ycdot P$)-constant deformations of Gorenstein surface singularities"Commentarii Mathematici Helvetici. (掲載受理).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tadashi Tomaru: "On some classes of weakly Kodaira singularities"Proceedings of the Franco-Japanese Luminy Conference of singularities. (Societe Mathematique de France). (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tomohiro Okuma: "On ($-P\cdot P$)-constant deformations of Gorenstein surface singularities"Commentarii Mathematici Helvetici. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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