1991 Fiscal Year Annual Research Report

多様体の代数的理論

Research Project

Project/Area Number	01302001
Research Institution	Osaka University
Principal Investigator	宮西正宜大阪大学, 理学部, 教授 (80025311)
Co-Investigator(Kenkyū-buntansha)	川又雄二郎東京大学, 理学部, 教授 (90126037) 上野健爾京都大学, 理学部, 教授 (40011655) 丸山正樹京都大学, 理学部, 教授 (50025459) 北岡良之名古屋大学, 理学部, 教授 (40022686) 小田忠雄東北大学, 理学部, 教授 (60022555)
Keywords	代数多様体 / ベクトル束 / CalabiーYou多様体 / ホッジ理論 / 周期写像 / 可換環 / 特異点
Research Abstract	1.研究代表者および分担者は多様体に関連するそれぞれの分担課題を中心とした研究を、研究協力者の協力を得て行った。 2.上記の研究成果のうち特に著しいものをテ-マ別に集めて、シンポジウムを企画、開催した。そのうち、平成3年度に開催したものは次の通りである。 (1)代数幾何学シンポジウム(京都大学理学部数学教室、10月1日-4日)代数多様体上のベクトル束に関連した新しい知見が報告された。 (2)可換環論シンポジウム(インテック大山研修センタ-、10月30日-11月2日)代数多様体を可換環論を通して研究することにより、その局所的性質や特異点に関する新知識が得られた。 (3)代数幾何学シンポジウム(兵庫県立城崎大会議館、11月4日-8日)代数多様体をめぐる種々の研究結果が報告された。 (4)代数幾何学とホッジ理論シンポジウム(京都大数理解析研究所、12月2日-6日)代数多様体の性質一般とホッジ理論に関する興味深い新知見が報告された。 3.世界各地における研究課題に関連する資料は、シンポジウムの機会を通して分担者・協力者の間に周知するようにした。 4.また、関連の深いシンポジウムには講演者を派遣するなどして研究協力した。 5.分担者間の連絡・討論を代表者が中心となって活発に行った。 6.上記2のシンポジウムを含めて、研究期間(平成元年-3年)に得られた成果のうちいくつかをまとめた報告集を印刷・配布した。その一覧は研究成果報告書にある。 3年間の研究期間を通じて、研究成果報告書にもあるように活発な研究活動が行われ、十分な成果が得られたと考える。多様体を代数的手法で研究することは一層発展することが期待され、最も有望な数学分野の一つである。

Research Products

(31 results)

All Other

All Publications

[Publications] MIYANISHI,Masayoshi: "Homology planes with quotient singularities" Journal of Mathematics,Kyoto University. 31. 755-788 (1991)
[Publications] MIYANISHI,Masayoshi: "Gorenstein del Pezzo surfaces,II" Journal of Algebra. (1992)
[Publications] GURJAR,R.V.: "Affine lines on logarithmic Qーhomology planes" Mathematische Annalen.
[Publications] ODA,Tadao: "Simple convex polytopes and the strong Lefschetz theorem" Journal of pure and Applied Algebra. 71. 265-286 (1991)
[Publications] ODA,Tadao: "Linear Gale transforms and GelfandーKapranovーZelevinskij decompositions" Tohoku Mathematical Journal. 43. 375-399 (1991)
[Publications] KITAOKA,Yoshiyuki: "A note on representation of positive definite binary quadratic forms by positive definite quadratic forms in 6 variables" Acta Arithmetica. 54. 317-322 (1990)
[Publications] KITAOKA,Yoshiyuki: "A note on Klingen's Eisenstein series" Abh.Math.Sem.Univ.Hamburg. 60. 95-114 (1990)
[Publications] MARUYAMA,Masaki: "On compactifications of the moduli space of instantons" International Journal of Mathematics. 1. 431-477 (1990)
[Publications] MARUYAMA,Masaki: "Moduli of parabolic stable bundles" Mathematische Annalen. (1992)
[Publications] KATSURA,Toshiyuki: "New besonization and conformal field theory over Z" Commun.Mathematical Physics. 121. 603-627 (1989)
[Publications] KAWAMATA,Yuujiro: "On the length of an extremal rational curve" Inventiones Mathematicae. 105. 609-611 (1991)
[Publications] KAWAMATA,Yuujiro: "Unobstructed deformationsーa remark on a paper of Z.Ran" Journal of Algebraic Geometry. (1992)
[Publications] SUWA,Tatsuo: "Dーmodules associated to complex analytic singular foliations" J.Fac.Sci.Univ.Tokyo Sect.IA Math.37. 297-320 (1990)
[Publications] SUWA,Tatsuo: "Finite determinacy of analytic foliation germs without formal integrating factors" Proc.Amer.Math.Soc.112. 989-997 (1991)
[Publications] FUJITA,Takao: "On singular Del Pezzo varieties" Proceedings of L'Aquilla meeting in Algebraic Geometry,Lecture Notes in Mathematics. 1417. 117-128 (1990)
[Publications] FUJITA,Takao: "On Del Pezzo fibrations over curves" Osaka Journal of Mathematics. 27. 229-245 (1990)
[Publications] SHIODA,Tetsuji: "MordellーWeil lattices of type E_8 and deformation of singularities" Lecture Notes in Mathematics. 1468. 177-202 (1991)
[Publications] SHIODA,Tetsuji: "An infinite family of elliptic curves over Q with large rank via Neron's method" Inventiones Mathematicae. 106. 109-119 (1991)
[Publications] IITAKA,Shigeru: "Group theory through computer programming" Proceedings of ICMIーCHINA Regional Conference on Mathematical Education. 3-24 (1991)
[Publications] WATANABE,Keiichi: "Regular Zーgraded rings" Proc.Fac.Sci.Tokai Univ.25. 1-8 (1990)
[Publications] WATANABE,Keiichi: "Fーreguler and Fーpure normal graded rings" J.Pure Appl.Algebra. 71. 341-350 (1991)
[Publications] MORI,Shigefumi: "Classification of threeーdimensional flips"
[Publications] NAGATA,Masayoshi: "A proof of the theorem of EakinーNagata" Proc.Japan Acad.67. 238-239 (1991)
[Publications] NAGATA,Masayoshi: "Some questions on euclid rings" Proc.Conf.Ordered Structure and Alg.Comput.Languages,Hong Kong 1991.
[Publications] MABUCHI,Toshiki: "Compactification of the moduli space of Einstein Kahler orbifolds" Adv.Stud.Pure Math.18. 359-384 (1990)
[Publications] MABUCHI,Toshiki: "Compactification of the moduli space of quartic del pezzo surfaces" Lecture Notes in Mathematics.
[Publications] SUMIHIRO,Hideyasu: "On the geometry of determinantal varieties associated to 2ーbundles on P^n"
[Publications] SUMIHIRO,Hideyasu: "A vanishing theorem for symmetric tensors of 2ーbundles on P^n and its applications"
[Publications] UMEMURA,Hiroshi: "Birational automorphism groups and the differential equations" Nagoya Math.Journal. 119. 1-80 (1990)
[Publications] UMEMURA,Hiroshi: "Second proof of the irreducibility of the first differential equation of Painleve" Nagoya Math.Journal. 117. 125-171 (1990)
[Publications] FUJITA,Takao: "Classification Theories of Polarized Varieties" Cambridge University Press, 205+xiv (1990)

1991 Fiscal Year Annual Research Report

多様体の代数的理論

Principal Investigator

宮西 正宜 大阪大学, 理学部, 教授 (80025311)

Research Products

[Publications] MIYANISHI,Masayoshi: "Homology planes with quotient singularities" Journal of Mathematics,Kyoto University. 31. 755-788 (1991)

[Publications] MIYANISHI,Masayoshi: "Gorenstein del Pezzo surfaces,II" Journal of Algebra. (1992)

[Publications] GURJAR,R.V.: "Affine lines on logarithmic Qーhomology planes" Mathematische Annalen.

[Publications] ODA,Tadao: "Simple convex polytopes and the strong Lefschetz theorem" Journal of pure and Applied Algebra. 71. 265-286 (1991)

[Publications] ODA,Tadao: "Linear Gale transforms and GelfandーKapranovーZelevinskij decompositions" Tohoku Mathematical Journal. 43. 375-399 (1991)

[Publications] KITAOKA,Yoshiyuki: "A note on representation of positive definite binary quadratic forms by positive definite quadratic forms in 6 variables" Acta Arithmetica. 54. 317-322 (1990)

[Publications] KITAOKA,Yoshiyuki: "A note on Klingen's Eisenstein series" Abh.Math.Sem.Univ.Hamburg. 60. 95-114 (1990)

[Publications] MARUYAMA,Masaki: "On compactifications of the moduli space of instantons" International Journal of Mathematics. 1. 431-477 (1990)

[Publications] MARUYAMA,Masaki: "Moduli of parabolic stable bundles" Mathematische Annalen. (1992)

[Publications] KATSURA,Toshiyuki: "New besonization and conformal field theory over Z" Commun.Mathematical Physics. 121. 603-627 (1989)

[Publications] KAWAMATA,Yuujiro: "On the length of an extremal rational curve" Inventiones Mathematicae. 105. 609-611 (1991)

[Publications] KAWAMATA,Yuujiro: "Unobstructed deformationsーa remark on a paper of Z.Ran" Journal of Algebraic Geometry. (1992)

[Publications] SUWA,Tatsuo: "Dーmodules associated to complex analytic singular foliations" J.Fac.Sci.Univ.Tokyo Sect.IA Math.37. 297-320 (1990)

[Publications] SUWA,Tatsuo: "Finite determinacy of analytic foliation germs without formal integrating factors" Proc.Amer.Math.Soc.112. 989-997 (1991)

[Publications] FUJITA,Takao: "On singular Del Pezzo varieties" Proceedings of L'Aquilla meeting in Algebraic Geometry,Lecture Notes in Mathematics. 1417. 117-128 (1990)

[Publications] FUJITA,Takao: "On Del Pezzo fibrations over curves" Osaka Journal of Mathematics. 27. 229-245 (1990)

[Publications] SHIODA,Tetsuji: "MordellーWeil lattices of type E_8 and deformation of singularities" Lecture Notes in Mathematics. 1468. 177-202 (1991)

[Publications] SHIODA,Tetsuji: "An infinite family of elliptic curves over Q with large rank via Neron's method" Inventiones Mathematicae. 106. 109-119 (1991)

[Publications] IITAKA,Shigeru: "Group theory through computer programming" Proceedings of ICMIーCHINA Regional Conference on Mathematical Education. 3-24 (1991)

[Publications] WATANABE,Keiichi: "Regular Zーgraded rings" Proc.Fac.Sci.Tokai Univ.25. 1-8 (1990)

[Publications] WATANABE,Keiichi: "Fーreguler and Fーpure normal graded rings" J.Pure Appl.Algebra. 71. 341-350 (1991)

[Publications] MORI,Shigefumi: "Classification of threeーdimensional flips"

[Publications] NAGATA,Masayoshi: "A proof of the theorem of EakinーNagata" Proc.Japan Acad.67. 238-239 (1991)

[Publications] NAGATA,Masayoshi: "Some questions on euclid rings" Proc.Conf.Ordered Structure and Alg.Comput.Languages,Hong Kong 1991.

[Publications] MABUCHI,Toshiki: "Compactification of the moduli space of Einstein Kahler orbifolds" Adv.Stud.Pure Math.18. 359-384 (1990)

[Publications] MABUCHI,Toshiki: "Compactification of the moduli space of quartic del pezzo surfaces" Lecture Notes in Mathematics.

[Publications] SUMIHIRO,Hideyasu: "On the geometry of determinantal varieties associated to 2ーbundles on P^n"

[Publications] SUMIHIRO,Hideyasu: "A vanishing theorem for symmetric tensors of 2ーbundles on P^n and its applications"

[Publications] UMEMURA,Hiroshi: "Birational automorphism groups and the differential equations" Nagoya Math.Journal. 119. 1-80 (1990)

[Publications] UMEMURA,Hiroshi: "Second proof of the irreducibility of the first differential equation of Painleve" Nagoya Math.Journal. 117. 125-171 (1990)

[Publications] FUJITA,Takao: "Classification Theories of Polarized Varieties" Cambridge University Press, 205+xiv (1990)

宮西正宜大阪大学, 理学部, 教授 (80025311)