• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

The Study of the moduli space of Riemann surfaces and the projective invariants

Research Project

Project/Area Number 13640051
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTsuruoka National College of Technology

Principal Investigator

UEMATSU Kazuhiro  Tsuruoka National College of Technology, Mechanical Engineering, Associate Professor, 機械工学科, 助教授 (00280339)

Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2002: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
KeywordsAbelian conformal field Theory / Fermion / Moduli space / Projective invariants / Schur Polynomials / 射影不変量 / 保型形式
Research Abstract

We tried to clarify the relations between the ring of projective invariants of algebraic curves and the coordinates or the automorphic forms of the moduli space Ag of abelian varieties. But we have had no new results even in the case of g=3. We will continue this research.
On the other hand, we have studied the abelian conformal field theory of N-pointed Riemann surfaces with Professor Ueno Kenji at Kyoto University because this study may give some information of the moduli space. We defined the complex vector space, which is named the abelian conformal block of an N-pointed Riemann surface by the two conditions. We tried to prove that the dimension of conformal block of any N-pointed Riemann surface is one. If we succeed, we can define the line bundle on the moduli space of N-pointed Riemann surfaces. But we were not able to prove this. There was a little gap. Then by reducing the two gauge conditions to one, we tried to reconstruct the abelian conformal field theory, but we have not finished yet.
In the study of abelian conformal field theory we construct the fermion operators acting on the polynomial ring with infinite indeterminants as differential operators. By proving the identities among Schur polynomials or differential polynomials, we directly showed that these operators satisfy the fermion relations. Now we attempt to generalize these relations and find new formula.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (4 results)

All Other

All Publications (4 results)

  • [Publications] 上松 和弘: "Schur多項式によるフェルミオンの実現"鶴岡工業高等専門学校研究紀要. 36. 41-46 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Uematsu Kazuhiro: "The Realization of Fermions by Schur Polynomials"Research Reports of Tsuruoka National College of Technology. 36. 41-46 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] 上松 和弘: "Schur多項式によるフェルミオンの実現"鶴岡工業高等専門学校研究紀要. 36. 41-46 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] 上松 和弘: "Schur多項式によるフェルミオンの実現"鶴岡工業高等専門学校研究紀要. 36. 41-46 (2001)

    • Related Report
      2001 Annual Research Report

URL: 

Published: 2001-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi