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1998 Fiscal Year Final Research Report Summary

Studies on Hodge Theory and Hypergeometric Functions

Research Project

Project/Area Number 09640010
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTHE UNIVERASITY OF TOKYO

Principal Investigator

KAWAMATA Yujiro  University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (90126037)

Co-Investigator(Kenkyū-buntansha) SAITO Takeshi  University of Tokyo, Graduate School of Mathematical Sciences, Associate Profess, 大学院・数理科学研究科, 助教授 (70201506)
KATSURA Toshiyuki  University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (40108444)
ODA Takayuki  University of Tokyo, Graduate School of Mathematical Sciences, Professor, 大学院・数理科学研究科, 教授 (10109415)
TERASOMA Tomohide  University of Tokyo, Graduate School of Mathematical Sciences, Associate Profess, 大学院・数理科学研究科, 助教授 (50192654)
Project Period (FY) 1997 – 1998
Keywordsalsebraic variety / pluricanonical form / Kodaira dimension / logarithmic form / multiplier ideal / canonical singularity / deformation / plurigenus
Research Abstract

In the course of the investigation of the structure of algebraic varieties, it is often very helpful to look at the pluricanonical forms on the given varieties. For example, the Kodaira dimension of a variety is the order of growth of the m-genus, the dimension of the vector space of m-canonical forms, as a function on the integer m. This is a fundamental invariant for the birational classification of algebraic varieties. We investigated the problem of comparing log pluricanonical forms on a given variety with pluricanonical forms on its subvariety.
Let X be a smooth algebraic variety and Y a smooth divisor. For example, Y is a compact algebraic manifold and X is the total space of its deformation family. We considered the problem of extending pluricanonical forms on Y to log pluricanonical forms on X.We defined sequences of multiplier ideal sheaves on X and Y, and the extension problem is reduced to the problem of the inclusion relationships among these ideals. We proved an extension theorem under some conditions. As applications. we proved that any deformations of canonical singularities are canonical, and that the plurigenus is constant on any deformation family of varieties of general type with only canonical singularities.

  • Research Products

    (15 results)

All Other

All Publications (15 results)

  • [Publications] 川又雄二郎: "On the extensim problem of plaricanonical forms" Contemporary Math.(予定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川又雄二郎: "Deformations of canonical sirgularitics" Journal of Amer.Math.Soc.(予定). (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川又雄二郎: "Subadjunction of log canonial divisors II" Amer,J.Math.120. 893-899 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 川又雄二郎: "On the cone of divisors of Calabi-Yanfiberspuces" Internat.J.Math.8. 665-687 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 寺杣友秀: "Cohomological Radon transform and mixed twisted E-poly." 数理解析研究所講究録. 999. 44-48 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 寺杣友秀: "Determinants of 9-hypergeometric functions." Mathematis che Zeitschrift. 226. 499-512 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 桂 利行: "代数幾何入門" 共立出版, 202 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Yujiro Kawamata: "On the extension problem of pluricanonical forms" math.AG/9809091 Contemporary Math.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yujiro Kawamata: "Index l covers of log terminal surface sigularities" math.AG/9802044 J.Alg.Geom.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yujiro Kawamata: "Deformations of canonical singularities" alg-geom/9712018 J.AMS.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yujiro Kawamata: "Subadjunction of log canonical divisors II" Amer.J.Math.120. 893-899 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yujiro Kawamata: "On the cone of divisors of Calabi-Yau fiber spaces" Internat.J.Math.8. 665-687 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tomohide Terasoma: "Cohomological Radon transform and mixed twisted E-poly" RIMS Kokyuroku. 999. 44-48 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Tomohide Terasoma: "Determinants of q-hypergeometric functions." Mathematische Zeitschrift. 226. 499-512 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Toshiyuki KATSURA: Introduction of Algebraic Geometry. KYOURITU SHUPPAN, 202 (1998)

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

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Published: 1999-12-08  

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