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1999 Fiscal Year Final Research Report Summary

Classification and structure of polarized varieties

Research Project

Project/Area Number 09440008
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Institute of Technology

Principal Investigator

FUJITA Takao  Department of Earth and Planetary Science, TOKYO INSTITUTE OF TECHNOLOGY, Professor, 理工学研究科, 教授 (40092324)

Co-Investigator(Kenkyū-buntansha) MIZUMOTO Shin-ichiro  Department of Earth and Planetary Science, TOKYO INSTITUTE OF TECHNOLOGY, Associate Prof., 理工学研究科, 助教授 (90166033)
TSUJI Hajime  Department of Earth and Planetary Science, TOKYO INSTITUTE OF TECHNOLOGY, Associate Prof., 理工学研究科, 助教授 (30172000)
ISHII Shihoko  Department of Earth and Planetary Science, TOKYO INSTITUTE OF TECHNOLOGY, Professor, 理工学研究科, 教授 (60202933)
KOBAYASHI Masanori  Faculty of Science, Tokyo Metropolitan Univ., Associate Prof., 理学部, 助教授 (60234845)
NAKAYAMA Chikara  Department of Earth and Planetary Science, TOKYO INSTITUTE OF TECHNOLOGY, Research Associate, 理工学研究科, 助手 (70272664)
Project Period (FY) 1997 – 1999
Keywordspolarized varieties / adjoint bundle / Kodaira energy
Research Abstract

The head investigator Fujita has classified non-singular polarized threefolds with Kodaira energy less than -1/2, and described precisely the structure of the adjoint fibrations. He further found out that the techniques of Kawachi-Masek in the study of base points of adjoint linear systems of normal polarized surfaces can be utilized also in the case of normal surfaces with Q-boundaries.
Investigator Ishii has found a sufficient condition for minimal models of singularities of certain type to be obtained by a weighted blow up, and proved that nondegenerate hypersurface singularities have minimal, canonical and log-canonical models. She further found a counter example to a conjecture by Reid on a characterization of hypersurface rational singularities by weights, and showed the existence of simple elliptic singularies not of known type. She showed also various important properties of the set of possible values of the invariant - KィイD12ィエD1 of normal surface singularities.
Investigator Tsu … More ji has established the theory of analytic Zariski decomposition, and constructed natural singular Hermitian metrics with positive curvature for line bundles. He applied this theory in the study of pluri-canonical systems of varities of general type and many problems including the abundance conjecture for minimal varieties of any dimensions.
Investigator Mizumoto has showed that there are good Eisenstein liftings between certain spaces of (quasi)-automorphic forms. He further showed various properties of certain L-functions and non-regular Eisenstein series related to SL(2, Z).
Investigator Nakayama has generalized classical theoris of etale cohomology to logarithmic structures. Further, he established basic theories of log geometry of complex analytic spaces, which was used to prove the degeneration of l-adic weight spectral sequences over arbitrary fields.
Investigator Kobayashi has studied the behaviours of real algebraic varieties under blowing up, especially in case of embedded curves in real plane. He also constructed an explicit example of a Calabi-Yau threefold with certain elliptic fibration whose set of real points is a SUSY 3-torus. Less

  • Research Products

    (42 results)

All Other

All Publications (42 results)

  • [Publications] T. Fujita: "On Kodaira energy and adjoint reduction of polarized three folds"Manuscripta Math.. 94. 211-229 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Fujita: "An appendix to Kawach-Masek's paper on global generation of adjoint bundles on normal surfaces"J. of Alg. Geom.. 7. 251-252 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] A. Futaki: "Functionals with cocycle conditions and Kahler-Einstein metrics of positive scalar curvature"Proc. Symp. In Hayama 1999 on several complex variables.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Ishii: "The weighted blowing ups of singularities with X =0"Studies in Adv. Math.. 75-82 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Ishii: "Minimal canonical and log-canonical models of hypersurface singulants"Contemporary Math.. 207. 63-77 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Chen and S. Ishii: "On -K^2 for normal surface singularities"International J. Math. 9. 653-668 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Ishii: "The minimal model theorem for divisors of toric varieties"Tohoku Math. J.. 51. 213-226 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] N. Kurokawa, R. Sasaki and H. Tanuma: "spectra of Categories"Proc. Japan Acad. 75-6. 92-95 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] J. Noguchi: "Nevanlinna - Cartan theory over function fields and a Diophantine equation"J. reine angew. Math.. 487. 61-83 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Mizumoto: "Nearly holomorphic Eisenstein liftings"Abh. Math. Sem. Univ. Hamburg. 67. 173-194 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Mizumoto: "Certain L - functions at S=1/2"Acta Arithmetica. 88. 51-66 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Tsuji: "Existence and applications of Analytic Zariski Decompositions"Trends in Math.. 253-271 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Tsuji: "Entire holomorphic curves and pluricanonical systems"Proc. Hayama Symp. On Several Complex Variables. 121-130 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Somekawa: "Log-syntomic regulators and P-adic polylogarithm"K - theory. 361. 1-29 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] C. Nakayama: "Logarithmic e tale cohomology"Math. Ann. 308. 365-404 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] C. Nakayama: "Nearly cycles for log smooth families"Compositio Math.. 112. 45-75 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Kajiwara and C. Nakayama: "Weights of the l-adic cohomology of a proper toric variety"Comm. In Algebra. 26. 4143-4147 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Kato and C. Nakayama: "Log Betti cohomology, log etale cohomology and log de Rham cohomology of log schemes ever (1)"Kodai Math. J.. 22. 161-186 (1999)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Kobayashi and T. C. Kuo: "Uniqueness of unibranched curve in IR^2 up to simple blowings up"Prac. Japan Acad.. 73. 97-99 (1997)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Kobayashi and T. C. Kuo: "On blow-analytic equivalence of embedded curve singularities"Real Analytic and Algebraic Singularities Pitman Research Notes. 381. 30-37 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M. Kobayashi: "A special Lagrangian 3-torus as a real slice"Integrable Systems and Algebraic Geometry. 315-319 (1998)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T. Fujita: "On Kodaira energy and adjoint reduction of polarized threefolds"manuscripta math. 94. 211-229 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Fujita: "An appendix to Kawachi-Masek's paper n global generation of adjoint bundles on normal surfaces"J. of Alg. Geom.. 7. 251-252 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Futani: "Functionals with cocycle conditions and Kahler-Einstein metrics of positive scalar curvature"Proc. Symp. in Hayama 1999 on several complex variables.

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Ishii: "The weighted blowing ups of singularities with k = 0"Studies in Adv. Math. 5. 75-82 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Ishii, Minami: "canonical and log-canonical models of hypersurface singularities"Contemporary Math. 207. 63-77 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Chen and S. Ishii: "on -KィイD12ィエD1 for normal suffice singularities"International J. Math. 9, No. 6. (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Ishii: "The minimal model theorem for divisors of toric varieties"Tohoku Math. J.. 51. 213-226 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] N. Kurokawa, R. Sasaki and H. Tanuma: "Spectra of categories"Proc. Japan Acd.. 75-6. 92-95 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] J. Noguchi: "Nevanlinna-Cartan theory over function fields and a Diophanrine equation"J. reine angew. Math.. 487. 61-83 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Mizumoto: "Nearly holomorphic Eisenstein liftings"Abh. Math. Sem. Univ. Hamburg. 67. 173-194 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Mizumoto: "Certain L-functions at s = 1/2"Acta Arithmetica. 88. 51-66 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Tsuji: "Existence and applications of Analytic Zariski Decompositions"Trends in Math.. 253-271 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Tsuji: "Entire holomorphic curves and pluricanonical systems"Proc. of Hayama Symposium on Several Complex Variables 1998. 121-130 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kobayashi and T. C. Kuo: "Uniqueness of unibranched curve in RィイD12ィエD1 up to simple blowings up"ProcJapan Acad.. 73, Ser. A. 97-99 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kobayashi and T. C. Kuo: "On blow-analytic equivalence of embedded curve singularities, in Real analytic and algebraic singularities (T. Fukuda et al. eds.)"Pitman Research Notes in Math. Series 381. 30-37 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Kobayashi: "A special Lagrangian 3-torus as a real slice, in Intergrable Systems and Algebraic Geometry"Proceedings of the Taniguchi Symposium Kobe/Kyoto 1997 (Saito, M., Shimizu, Y. and Ueno, K. eds.), World Scientific. 315-319 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] C. Nakayama: "Logarithmic etale cohomology"Math. Ann.. 308. 365-404 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] C. Nakayama: "Nearby cycles for log smooth families"Compositio Math.. 112. 42-75 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Kajiwara and C. Nakayama: "Weights of the l-adic cohomology of a porper toric vaiety"Comm. in Algebra. 26. 4143-4147 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Kato and C. Nakayama: "Log Betti cohomoloty, log etale cohomology, and log de Rham cohomology of log schemes over C"Kodai Math. J.. 22. 161-186 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] S. Somekawa: "Log-syntomic regulators and p-adic polylogarithm"K-theory. 361. 1-29 (1998)

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

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Published: 2001-10-23  

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