1990 年度実績報告書

多様体の代数的理論

研究課題

研究課題/領域番号	01302001
研究機関	大阪大学
研究代表者	宮西正宜大阪大学, 理学部, 教授 (80025311)
研究分担者	川又雄二郎東京大学, 理学部, 教授 (90126037) 丸山正樹京都大学, 理学部, 教授 (50025459) 上野健爾京都大学, 理学部, 教授 (40011655) 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)
キーワード	代数多様体 / 代数群 / ホッジ理論 / ア-ベル多様体 / 可換環 / 特異点 / 半群
研究概要	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。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。 (1)代数群とその周辺シンポジウム(京都大数理解析研究所、5月28ー31日)代数群の整数論的また幾何学的性質に関して新しい知見を得た。 (2)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、7月9ー13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)可換環論シンポジウム(京都府立ゼミナ-ルハウス、10月30日ー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。 (4)代数幾何学シンポジウム(兵庫県立城崎大会議館、11月19ー23日)代数多様体をめぐる種々の研究結果が報告された。 3.世界数学者会議(8月21ー29日)が京都で開催されたが、その前後に開催された国際集会に研究協力者を派遣したり、講演を依頼するなどして支援した。 (1)代数幾何と解析幾何(東京都立大学学館と第百生命野沢研修センタ-、8月13ー17日)多数の外国人参加者があった。 (2)半群論国際研究集会(立命館大学末川記念館、8月30日ー9月1日) 4.ホッジ理論とア-ベル多様体の研究者の研究を援助した。 5.分担者間の連絡、討論を活発に行い、よい研究集会を企画できた。 6.上記の2の(3)と(4)に関連して、目ざましい結果を報告集に収録配布した。

研究成果

(34件)

すべてその他

すべて文献書誌 (34件)

[文献書誌] MIYANISHI,Masayoshi: "Finite group scheme actions on the affine plane" Journal of pure and applied algebra. (1991)
[文献書誌] MIYANISHI,Masayoshi: "Qーhomology planes with C^<**>ーfibrations" Osaka Journal of Mathematics. 28. (1991)
[文献書誌] MIYANISHI,Masayoshi: "Absence of the affine line on the homology planes" Journal of Mathematics,Kyoto University.
[文献書誌] ODA,Tadao: "Simple convex polytopes and the strong Lefschetz theorem" Journal of pure and applied algebra. (1991)
[文献書誌] ODA,Tadao: "Linear Gale transforms and Gelfand Kapranov Zelevinskij decompositions" Tohoku Math.J.
[文献書誌] MORI,Shigefumi: "Birational classification of algebraic 3ーfolds;Announcement" American J.Mathematics.
[文献書誌] MARUYAMA,Masaki: "On compactifications of the moduli space of instantons" International J.Mathematics. (1991)
[文献書誌] MARUYAMA,Masaki: "Limits of instantons"
[文献書誌] KAWAMATA,Yujiro: "Small contractions of four dimensional algebraic manifolds" Math.Ann.284. 595-600 (1989)
[文献書誌] KAWAMATA,Yujiro: "Boundedness of QーFano threefolds" Contemporary Mathematics. (1991)
[文献書誌] SHIODA,Tetsuji: "MordellーWeil lattices and sphere packings" Amer.J.Math.
[文献書誌] SHIODA,Tetsuji: "Construction of elliptic curves over Q(t) with high rank via the invariants of the Weyl groups" Proc.Japan Acad.(1990)
[文献書誌] KITAOKA,Yoshiyuki: "Some remarks on representations of positive definite quadratic forms" Nagoya Math.J.115. 23-41 (1989)
[文献書誌] KITAOKA,Yoshiyuki: "A result on qーseries and its application to quadratic forms" J.Number Theory. 34. 54-62 (1990)
[文献書誌] MUKAI,Shigeru: "Polarized K3 surfaces of genus 18 and 20" Proc.of the conference on Vector bundles and Special projective embeddings,Bergen.
[文献書誌] MUKAI,Shigeru: "Fano 3ーfolds" Proc.of the conference on Projective Geometry,Trieste 1989.
[文献書誌] UENO,Kenji: "Conformal field theory on universal family of stable curves with gauge symmetries" Advanced Studies in Pure Mathematics. 19. 459-565 (1989)
[文献書誌] UENO,Kenji: "Formal groups and conformal field theory over Z" Advanced Studies in Pure Mathematics. 19. 347-366 (1989)
[文献書誌] NAGATA,Masayoshi: "Some remarks on the twoーdimensional Jacobian conjecture" Chinese J.Math.17. 1-7 (1989)
[文献書誌] NAGATA,Masayoshi: "Some questions on Z[√<14>]" Proc.of the conference on Algebraic Geometry and its appl.in honor of Prof.Abhyankar.
[文献書誌] MABUCHI,Toshiki: "An algebraic character associated with the Poisson brackets" Advanced Studies in Pure Mathematics. 18. 339-358 (1990)
[文献書誌] MABUCHI,Toshiki: "Compactification of the moduli space of Einstein Ka^^¨hler orbifolds" Advanced Studies in Pure Mathematics. 18. 359-384 (1990)
[文献書誌] UMEMURA,Hiroshi: "Second proof of the irreducibility of the first differential equation of Painleve^^´" Nagoya Math.J.117. 125-171 (1990)
[文献書誌] UMEMURA,Hiroshi: "Birational automorphism groups and the differential equations" Nagoya Math.J.119. 1-80 (1990)
[文献書誌] SUMIHIRO,Hideyasu: "On the geometry of determinantal varieties associated to 2ーbundles on P^n"
[文献書誌] WATANABE,Keiichi: "Regular Zーgraded rings" Proc.Fac.Sci.Tokai Univ.25. (1990)
[文献書誌] FUJITA,Takao: "On Del Pezzo fibrations over curves" Osaka J.Math.27. 229-245 (1990)
[文献書誌] ENDO,Shizuo: "Nonーrationality of algebraic tori of norm type and its application to generic division rings" Proc.Symp.Ring Theory. 22. 17-22 (1989)
[文献書誌] KATO,Kazuya: "Logarithmic structures of FontaineーIllusie" Amer.J.Math.
[文献書誌] SUWA,Tatsuo: "Determinacy of complex analytic foliation germs without integrating factors" Proc.Amer.Math.Soc.
[文献書誌] 宮西正宜: "代数幾何学" 裳華房,数学選書10, (1990)
[文献書誌] ODA,Tadao: "Introduction to Algebraic Singularities (with Taichi Ambai)" The Institute of Mathematical Sciences Lecture Notes 2, (1991)
[文献書誌] FUJITA,Takao: "Classification Theories of Polarized Varieties" Cambridge Univ.Press London Math.Soc.Lecture Note Series 155, (1990)
[文献書誌] 飯高茂: "Prologで作る数学の世界" 朝倉書店, (1990)

1990 年度 実績報告書

多様体の代数的理論

研究代表者

宮西 正宜 大阪大学, 理学部, 教授 (80025311)

研究成果

[文献書誌] MIYANISHI,Masayoshi: "Finite group scheme actions on the affine plane" Journal of pure and applied algebra. (1991)

[文献書誌] MIYANISHI,Masayoshi: "Qーhomology planes with C^<**>ーfibrations" Osaka Journal of Mathematics. 28. (1991)

[文献書誌] MIYANISHI,Masayoshi: "Absence of the affine line on the homology planes" Journal of Mathematics,Kyoto University.

[文献書誌] ODA,Tadao: "Simple convex polytopes and the strong Lefschetz theorem" Journal of pure and applied algebra. (1991)

[文献書誌] ODA,Tadao: "Linear Gale transforms and Gelfand Kapranov Zelevinskij decompositions" Tohoku Math.J.

[文献書誌] MORI,Shigefumi: "Birational classification of algebraic 3ーfolds;Announcement" American J.Mathematics.

[文献書誌] MARUYAMA,Masaki: "On compactifications of the moduli space of instantons" International J.Mathematics. (1991)

[文献書誌] MARUYAMA,Masaki: "Limits of instantons"

[文献書誌] KAWAMATA,Yujiro: "Small contractions of four dimensional algebraic manifolds" Math.Ann.284. 595-600 (1989)

[文献書誌] KAWAMATA,Yujiro: "Boundedness of QーFano threefolds" Contemporary Mathematics. (1991)

[文献書誌] SHIODA,Tetsuji: "MordellーWeil lattices and sphere packings" Amer.J.Math.

[文献書誌] SHIODA,Tetsuji: "Construction of elliptic curves over Q(t) with high rank via the invariants of the Weyl groups" Proc.Japan Acad.(1990)

[文献書誌] KITAOKA,Yoshiyuki: "Some remarks on representations of positive definite quadratic forms" Nagoya Math.J.115. 23-41 (1989)

[文献書誌] KITAOKA,Yoshiyuki: "A result on qーseries and its application to quadratic forms" J.Number Theory. 34. 54-62 (1990)

[文献書誌] MUKAI,Shigeru: "Polarized K3 surfaces of genus 18 and 20" Proc.of the conference on Vector bundles and Special projective embeddings,Bergen.

[文献書誌] MUKAI,Shigeru: "Fano 3ーfolds" Proc.of the conference on Projective Geometry,Trieste 1989.

[文献書誌] UENO,Kenji: "Conformal field theory on universal family of stable curves with gauge symmetries" Advanced Studies in Pure Mathematics. 19. 459-565 (1989)

[文献書誌] UENO,Kenji: "Formal groups and conformal field theory over Z" Advanced Studies in Pure Mathematics. 19. 347-366 (1989)

[文献書誌] NAGATA,Masayoshi: "Some remarks on the twoーdimensional Jacobian conjecture" Chinese J.Math.17. 1-7 (1989)

[文献書誌] NAGATA,Masayoshi: "Some questions on Z[√<14>]" Proc.of the conference on Algebraic Geometry and its appl.in honor of Prof.Abhyankar.

[文献書誌] MABUCHI,Toshiki: "An algebraic character associated with the Poisson brackets" Advanced Studies in Pure Mathematics. 18. 339-358 (1990)

[文献書誌] MABUCHI,Toshiki: "Compactification of the moduli space of Einstein Ka^^¨hler orbifolds" Advanced Studies in Pure Mathematics. 18. 359-384 (1990)

[文献書誌] UMEMURA,Hiroshi: "Second proof of the irreducibility of the first differential equation of Painleve^^´" Nagoya Math.J.117. 125-171 (1990)

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

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

[文献書誌] WATANABE,Keiichi: "Regular Zーgraded rings" Proc.Fac.Sci.Tokai Univ.25. (1990)

[文献書誌] FUJITA,Takao: "On Del Pezzo fibrations over curves" Osaka J.Math.27. 229-245 (1990)

[文献書誌] ENDO,Shizuo: "Nonーrationality of algebraic tori of norm type and its application to generic division rings" Proc.Symp.Ring Theory. 22. 17-22 (1989)

[文献書誌] KATO,Kazuya: "Logarithmic structures of FontaineーIllusie" Amer.J.Math.

[文献書誌] SUWA,Tatsuo: "Determinacy of complex analytic foliation germs without integrating factors" Proc.Amer.Math.Soc.

[文献書誌] 宮西 正宜: "代数幾何学" 裳華房,数学選書10, (1990)

[文献書誌] ODA,Tadao: "Introduction to Algebraic Singularities (with Taichi Ambai)" The Institute of Mathematical Sciences Lecture Notes 2, (1991)

[文献書誌] FUJITA,Takao: "Classification Theories of Polarized Varieties" Cambridge Univ.Press London Math.Soc.Lecture Note Series 155, (1990)

[文献書誌] 飯高 茂: "Prologで作る数学の世界" 朝倉書店, (1990)

1990 年度実績報告書

宮西正宜大阪大学, 理学部, 教授 (80025311)

[文献書誌] 宮西正宜: "代数幾何学" 裳華房,数学選書10, (1990)

[文献書誌] 飯高茂: "Prologで作る数学の世界" 朝倉書店, (1990)