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1994 Fiscal Year Final Research Report Summary

Algebraic and Geometric Study on the Structure of Moduli Spaces

Research Project

Project/Area Number 05452003
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

MARUYAMA Masaki  Fac.of Science, Kyoto Univ., Professor, 理学部, 教授 (50025459)

Co-Investigator(Kenkyū-buntansha) KONO Akira  Fac.of Science, Kyoto Univ., Professor, 理学部, 教授 (00093237)
NISHIDA Goro  Fac.of Science, Kyoto Univ., Professor, 理学部, 教授 (00027377)
YOSHIDA Hiroyuki  Fac.of Science, Kyoto Univ., Professor, 理学部, 教授 (40108973)
UENO Kenji  Fac.of Science, Kyoto Univ., Professor, 理学部, 教授 (40011655)
HIJIKATA Hiroaki  Fac.of Science, Kyoto Univ., Professor, 理学部, 教授 (00025298)
Project Period (FY) 1993 – 1994
KeywordsModuli / Vector Bundle / Stable Sheaf / Hermit-Einstein connection / Instanton / Parabolic Stable Sheaf / Betti Number / Projective Plane
Research Abstract

Moduli in geometry is a set of geometric objects endowed with the universal geometric structure. It is known that not only a moduli space itself is a rich geometric object but also it is often a useful tool in studying geometry. For example the moduli space of Hermit-Nesting connections reflects strongly the differential geometric nature of the base manifold. On the other hand, as the fact that a Hermit-Nesting connection is nothing but a stable vector bundle shows us, we realize that moduli spaces constructed independently in different fields sometimes coincide with each other. This has been promoting direction of studying the theory of moduli spaces from various viewpoints. In this project we have carried out our study on classifying spaces, moduli of various connections and moduli of vector bundles, in cooperation with the specialists of topology, differential geometry, number theory, algebraic geometry and commutative algebra in our department. We have got the following results.
1.We completed the computation of Betty numbers of the moduli spaces of stable sheaves of rank 2 on the projective plane and furthermore we got a similar results on ruled surfaces.
2.We could clarify an interesting relationship between parabolic stable vector bundles on the projective plane and instantaneous. Using this we could prove that the moduli spaces of instantaneous are connected.
3.The standard of the moduli spaces of stable sheaves of rank 2 the on projective plane are dominated by those of the moduli spaces of parabolic stable vector bundles. They are related under a generalization of the elementary transformation of vector bundles.
4.We could develop deep study of reflexive sheaves on surfaces with rational double points and their deformations.
5.We applied our results on vector bundles to the theory of conformal field theory.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] 丸山正樹: "Instantons and parabolic sheaves" Proc.Internat.Collog.on Geomerty and Analysisに掲載予定.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 河野明: "A topological proof of Bott periodicity thaeum and characterization of BU" J.of Math.Kyoto Univ.34. 873-880 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 齋藤政彦: "On Modell-Weil lattries of higher genus fibrations on rational surfaces" J.of Math.Kyoto Univ.34. 859-872 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 上野健爾: "On conformal field theory" Proc.of Durham Symp in Vector Bumdlesに掲載予定.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉岡康太: "The Betti numbers of the moduli spaces of stoble sheaves of rank2 on P^2" J reine angew.Math. 453. 193-220 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 土方弘明: "Bass orders in non semisimple algelras" J.of Math.Kyoto Univ.34. 797-838 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Masaki MARUYAMA: "Instantons and parabolic sheaves" Proc.Internet. Collog on Geometry and Analysis. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira KONO: "A topological proof of Botl periodicity theorem and characterization of BU" J.of Math.Kyoto Univ.Vol.34. 873-880 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masahiko SAITO: "On Modell-Weil lattices of higher genus fibrations on rational surfaces" J.of Math.Kyoto Univ.Vol.34. 859-872 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kenji UENO: "On conformal field theory" Proc.of Durham Symp on Vector Bundles. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Kota YOSHIOKA: "The Betli numbers of moduli spaces of stable sheaves of rank 2 on IP^2" J.reine angew. Math. Vol.453. 193-220 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroaki HIJIKATA: "Bass orders in non se misimple algebras" J.of Math.Kyoto Univ.Vol.34. 797-838 (1994)

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

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Published: 1996-04-15  

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