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Variation of Hodge structures and hypergeometric functions

Research Project

Project/Area Number 11640012
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionUniversity of Tokyo

Principal Investigator

TERASOMA Tomohide  University of Tokyo, Departement of Mathematical Science, Associate Professor, 大学院・数理科学研究科, 助教授 (50192654)

Co-Investigator(Kenkyū-buntansha) KAWAMATA Yujiro  University of Tokyo, Departement of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (90126037)
OGUISO Keiji  University of Tokyo, Departement of Mathematical Science, Associate Professor, 大学院・数理科学研究科, 助教授 (40224133)
SAITO Takeshi  University of Tokyo, Departement of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (70201506)
KATSURA Toshiyuki  University of Tokyo, Departement of Mathematical Science, Professor, 大学院・数理科学研究科, 教授 (40108444)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
KeywordsHypergeometric functions / Toric geometry / Selberg integral / Multiple Zeta Value / トーリック幾何学 / ホッジ理論 / 代数的対応
Research Abstract

In the beginning of this research period, we are planning to study the relation between critical values and topological cycles for a family of toric hypersurfaces. This relateion is completely made clear. More concretely, we study them by constructing a compactification of the universal family of toric hypersurfaces in terms of convex bodies. We give an explicit comact family over the compactification of moduli associated to the secondary polytope. Using this construction, we found a correspondece between the stable cycles assciated to critical points and a formal expansion of hypergeometric functions.
Another theme of our research is on the expansion of Selberg integral with resepect to the complex exponent parameter. We obtain a complete result on this subject. We proved that the coefficient of the expansion is expressed as a linear combination of multiple zera values. The differential forms that we should consider is determined combinatorially and it happens to be equal to β-nbc base after Falk-Terao. We expect further developement in this directions.

Report

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

    (20 results)

All Other

All Publications (20 results)

  • [Publications] T.Terasoma: "Convolution theaem foron-degenerate maps and comportesingular ties"J.Algebraic Geom.. 9.no2. 265-287 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Terasoma: "Selberg integrals and multiple zeta values"to appear from comporition math..

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Saito-T.Terasoma: "Determinant of period in tegrals"J.Amer.Math.Soc.. 10no4. 865-937 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Oguiso-T.Petenell: "Calabi Yau three folds with positive chern clars"Comm in Analysis and Geometry. 6. 153-172 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Kawamato: "On the extension problem of pluricanonical forms"Contemporary math.. 241. 193-207 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Katyure-Gv.d Geer: "On a stratification of the moduli of k3 surfaces"J.European math.Soc.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Terasoma: "Convolution theromre for non-dengenerate maps and composite singularities"J.Algebraic Geom.. vol 9.no.2. 265-287 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Terasoma: "Selberg integrals and multiple zeta values"Compositio Math.. (to appear.).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Saito-T.Terasoma: "Determinant of period integral"J.Amer.Math.Soc.. vol 10 no.4. 865-937 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Oguiso-T.Peternell: "Calabi Yau threefolds with positive Chern class, Comm."in Analysis and Geometry. vol 6. 153-172 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.Kawamata: "On the extension problem of pluricanonical forms"Contemporary maht.. Vol 241. 193-207 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Katsura-G.v.d.Geer: "On a stratification of the moduli of K3 surfaces"J.European Math.Soc.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Terasome,T.: "Convolution theorem for non-degenerate maps and c-sing."J.Algebraic Geometry. 9 no2. 265-287 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Shioda,T.-Terasoma,T.: "Existence of simple Jacobian naneties of g=gems, rk=49.5"Amer.J.Math.. 121 no1. 65-72 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] Saito,T.: "The sign of the functional e9.of the L-fn. of orth. motive"Inventiones Math.. 120. 119-142 (1995)

    • Related Report
      2000 Annual Research Report
  • [Publications] Oguiso,K.: "On K3 surface admtting finite non symplectic grp. act."J.Math.Sci.Univ.of Tokyo. 5. 273-297 (1998)

    • Related Report
      2000 Annual Research Report
  • [Publications] Tomohide Terasoma: "Selberg Integral and Multiple ZetaValues"Compositio Mathematica. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Tomohide Terasoma: "Convolution theory for nondegenerate maps"Journal of Algebraic Geonetry. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] G.Vandu Geer-T. Katsura: "On a stratification of the moduli of K3 surfaces"J. of European Mathemetical Society. (to appear).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Kawamata: "On the extension problem of pluricanovical forms"Contemporary Math.. (to appear).

    • Related Report
      1999 Annual Research Report

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

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