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Research on Characteristic Classes of Singular Varieties

Research Project

Project/Area Number 11440014
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHOKKAIDO UNIVERSITY

Principal Investigator

SUWA Tatsuo  Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40109418)

Co-Investigator(Kenkyū-buntansha) ISHIKAWA Goo  Hokkaido Univ. Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (50176161)
IZUMIYA Shuichi  Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (80127422)
NAKAMURA Iku  Hokkaido Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (50022687)
OKA Mutsuo  Tokyo Metropolitan Univ. Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (40011697)
SHIMADA Ichiro  Hokkaido Univ. Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (10235616)
河澄 響矢  東京大学, 大学院・数理科学研究科, 助教授 (30214646)
與倉 昭治  鹿児島大学, 理学部, 教授 (60182680)
Project Period (FY) 1999 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥11,800,000 (Direct Cost: ¥11,800,000)
Fiscal Year 2001: ¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2000: ¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 1999: ¥4,700,000 (Direct Cost: ¥4,700,000)
Keywordssingular varieties / localization of characteristic classes / Schwartz-MacPherson class / Fulton-Johnson class / Milnor class / multiplicity / coherent sheaves / Riemann-Roch theorem / 特性類の局所化 / Fulton-Johnson類 / Milnor数 / Riemanu-Rochの定理
Research Abstract

Directed by the head investigator Suwa, the research on characteristic of singular varieties, in particular the theory of Milnor classes and related topics have been performed, as described in the research proposal, We obtained an explicit formula for the Minor class of a non- singular component of singular variety, the notion of the homology Chern class is introduced. The Riemann-Roch theorem for embeddings of singular varieties are proved arid used to compute the Chern class of the tangent sheaf of a singular variety. As an application of the theory of localization of characteristic classes, we defined, for functions on singular varieties the notion of multiplicity at the singularity, gave the method to compute them and proved, in the global situation, the "multiplicity formula", which generalized well-known classical formula in the non-singular case. We also gave a direct and geometric proof of the Lefschetz fixed point formula for the de Rham and Dolbeault complexes.
The other investigators collaborated in the above projects and also obtained many other results in the subjects such as : the moduli space of Abelian varieties, me McKay correspondence of simple singularities, developable surfaces of curves in the Euclidean space and classification of singularities of Dalboux sphere representations, stability of singular Lagrangian varieties, singular fibers of elliptic K3 surges and the torsion subgroup of the Mordell-Weli group, geometry of sextic curves of torus type and the geometry of dual curves, an alternative proof of the algebraic independence of the Monta-Mumfoixl classes, parital answer to the Akita conjecture on the mapping class group.

Report

(4 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • 1999 Annual Research Report
  • Research Products

    (30 results)

All Other

All Publications (30 results)

  • [Publications] T.Suwa: "Milnor classes of local complete intersections"Transactions of Amer. Math. Soc.. 354. 1351-1371 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] I.Nakamura: "Moduli space of elliotic curves with Heidelberg level str."Progress in Math, Biakhauser. 195. 299-324 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] I.Nakamura: "Hilbert schemes of abelian group orbits"J. Alg. Geometry. 10. 757-779 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] G.Ishikawa: "Solution surfaces of Monge-Ampere equations"Dill. Geom. and its. Applications. 14. 113-124 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] I.Shimada: "Lattices of algebraic cycles on Fermat varieties"Proc. London Math. Soc.. 82. 131-172 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M.Oka: "Another involution on aoduli of sextics"Kodai J. Math.. 24. 26-30 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T. Suwa: "Milnor classes of local complete intersections"Transactions Amer. Math. Soc.. 354. 1351-1371 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] I. Nakamura: "Moduli space of elliptic curves with Heisenberg level structure"Moduli of Abelian Varieties, Proceedings of Texel conference 1999, Progress in Math.. 195, Birkhauser. 299-324 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] I. Nakamura: "Hilbert schemes of abelian group orbits"Jour. Alg. Geom.. 10. 757-779 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] G. Ishikawa: "Solution surfaces of the Monge-Ampere equation"Differential Geometry and its Application. 14. 113-124 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] I. Shimada: "Lattices of algebraic cycles on Fermat varieties in positive characteristics"Proc. London Math. Soc.. 82. 131-172 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Oka: "Another involution on moduli of sextics"Kodai J. Math.. 24. 26-30 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] T.Suwa: "Milnor classes of local complete intersections"Transactions of Amer, Math, Soc.. 354. 1351-1371 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] I.Nakamura: "Moduli space of elliptic curves with Heisenberg level str."Progress in Math. Birkhauser. 195. 299-324 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] I.Nakamura: "Hilbert scheame of abelian group orbits"J. Alg. Geometry. 10. 757-779 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] G.Ishikawa: "Solution surfaces of Monge-Ampere equation"Difl. Geom. and its Applications. 14. 113-124 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] I.Shimada: "Lattices of algebraic cycles on Format varieties"Proc. London Math. Soc.. 82. 131-172 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] M.Oka: "Another involution on moduli of sextics"Kodai J. Math.. 24. 26-30 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] T.Suwa: "Nash residues of singular holomorphic foliations"Asian J.Math.. 4. 37-50 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Suwa: "Characteristic classes of coherent sheaves on singular varieties"Singularities-Sapporo 1998, ASPM. 29. 279-297 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] I.Nakamura: "Hilbert scheme of G-orbits in dimension three"Asian J.Math. 4. 51-70 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] S.Izumiya: "The lightcone Gauss map and the lightcone developable of a space like curves in Minkuski 3-Space"Glasgow Math.J.. 42. 75-89 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] G.Ishikawa: "Topological classification of the taugent developables of space curves"J.London Math.Soc.. 62. 583-598 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] M.Oka: "Geometry of cuspidal sextics and their dual curves"Singularties-Sapporo 1998, ASPM. 29. 245-277 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T. Suwa: "Generalization of variations and Baum-Bott residues for holomorphic foliations on singular varieties"Intern. J. Math.. 10. 367-384 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] T. Suwa: "Milnor numbers and classes for local complete intersections"Proc. Japan Acad.. 75. 179-183 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] I. Nakamura: "Stability of degenerate abelian varieties"Invent. Math.. 136. 659-715 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S. Izumiya: "A time-like surface in Minkowsk's 3-space whicd contains light-like lines"Journal of Geometry. 64. 95-101 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] M. Oka: "Flex curves and their applications"Geometriae Dedicata. 75. 67-100 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] S. Yokura: "On a Verdier-type Riemann-Roch for Chern-Schwartz-MacPherson class"Topology and its Applications. 94. 315-327 (1999)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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