1989 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	永田雅宜京都大学, 理学部, 教授 (00025230) 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) 森重文名古屋大学, 理学部, 教授 (00093328) 小田忠雄東北大学, 理学部, 教授 (60022555)
キーワード	代数曲面 / 3次元代数多様体 / 算術的代数多様体 / Hodge(ホッヂ)理論 / 共形場理論 / 特異点 / 半群 / 可換環
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なった。 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、シンポジウムを企画、開催した。 (1)半群論とその周辺シンポジウム(京都産業大、10月6-7日)可換環論や組合せ代数幾何学に於て半群の果たす役目が重要になる。 (2)可換環論シンポジウム(岐阜市厚生年金健康福祉センタ-・サンピア岐阜、11月8-11日)代数多様体の局所的性質、特に特異点に関連して新知見が得られた。 (3)代数幾何学ミニシンポジウム(東大理、12月21-22日)若手研究者を主体とした集会で、代数局面、算術的代数多様体、多様体の被覆に関連して、非常に興味深い結果が報告された。 (4)代数幾何学シンポジウム(兵庫県城崎町兵庫県立城崎大会議館)代数多様体および複素多様体に関する、日本における今年度第一線の研究発表がなされた。可換環についても新知見が報告された。 (5)群作用シンポジウム(東京電機大理工、3月22-24日)群作用の線形化、代数多様体の基本群、不変式論等について研究の現状が報告された。 3と4.Hodge理論、共形場理論、3次元代数多様体、微分体のガロア理論、特異点の解析的理論に関連して研究者を派遣し、有益な情報を得た。研究連絡は小数の研究者を特定の大学に派遣することによって行なったが、次年度以降、有望な課題を取り上げ、規模を広げて研究したい。 5.分担者間の連絡、討論を活発に行ない、よい研究集会を企画できた。 6.上記(1)、(3)、(4)に関連して、目ざましい結果を報告集に収録、配布した。(5)についても、次年度に報告集を作製したい。

研究成果

(37件)

すべてその他

すべて文献書誌 (37件)

[文献書誌] MIYANISHI,Masayoshi: "Finite equivalence relations on algebric varieties" Journal of pure and applied algebra. 57. 83-91 (1989)
[文献書誌] MIYANISHI,Masayoshi: "Homology planes with quotient singularities" J.Math.Kyoto.Univ.
[文献書誌] MIYANISHI,Masayoshi: "Q-homology planes with C^<**>-fibrations" Osaka J.Math.
[文献書誌] ODA,Tadao: "Simple convex polytopes and the strong Lefschetz theorem" J.Pure Appl.Algebra,special issue dedicated to Professor Hideyuki Matsumura on his sixtieth birthday. (1990)
[文献書誌] ODA,Tadao: "Geometry of toric varieties" Proc.Intern.Conf.on Algebraic Groups and Applications,Univ.of Hyderabad 1989.
[文献書誌] ODA,Tadao: "Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions"
[文献書誌] MORI,Shigefumi: "Flips in families"
[文献書誌] KITAOKA,Yoshiyuki: "Forier coefficients of certain Eisenstein series" Proc.of Japan Acad.65. 253-255 (1989)
[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] MUKAI,Shigeru: "Bireqular classification of Fano threefolds and Fano manifolds of coindex 3" Proc.Nat.Acad.Sci.USA. 86. 3000-3002 (1989)
[文献書誌] YASHINO,Yuji: "Modules with Linear resolution over a polynomial ring in two variables" Nagoya Math.J.113. 89-98 (1989)
[文献書誌] HIBI,Takayuki: "What can be said about pure O-sequences?" J.Combin.Theory,Ser.A. 50. 319-322 (1989)
[文献書誌] KATSURA,Toshiyuki: "New bosonization and conformal field theory" Commun.Math.Phys.121. 603-627 (1989)
[文献書誌] TSUCHIYA,Akihiro: "Coformal field theory on moduli family of stable curves with gauge symmetries" Advanced studies in pure math.19. 459-565 (1989)
[文献書誌] KATSURA,Toshiyuki: "Formal groups and conformal field theory over Z" Advanced studies in pure math.19. 347-366 (1989)
[文献書誌] NAGATA,Masayoshi: "Some remarks on the two-dimensional Jacobian Conjecture" Chinese Journ.of Math.17. 1-7 (1989)
[文献書誌] HIJIKATA,Hiroaki: "Orders in quaternion algebras" J.reine angew.Math.394. 59-106 (1989)
[文献書誌] MARUYAMA,Masaki: "On compactifications of moduli space of instantons"
[文献書誌] MARUYAMA,Masaki: "Limits of instantons"
[文献書誌] KAWAMATA,Yujiro: "Small contractions of four dimensional algebraic maniforlds" Math.Ann.284. 595-600 (1989)
[文献書誌] KAWAMATA,Yujiro: "Boundedness of Q-Fano threefolds"
[文献書誌] KAWAMATA,Yujiro: "Moderate degenerations of algebraic surfaces"
[文献書誌] FUJITA,Takao: "On Del Pezzo fibrations over curves" Osaka J.Math.27. (1990)
[文献書誌] FUJITA,Takao: "On adjoint bundles of ample vector bundles"
[文献書誌] SHIODA,Tetsuji: "Mordell-Weil Lattices and Galois representations I,II,III" Proc.Japan Acad.65A. 268-271,296-303 (1989)
[文献書誌] SHIODA,Tatsuji: "Construction of elliptic curves over Q(t)with high rank" Proc.Japan Acad.(1990)
[文献書誌] SUMIHIRO,Hideyasu: "On the geometry of determinantal varieties associated to 2-bundles on P^n"
[文献書誌] UMEMURA,Hiroshi: "Second proof of the irreducibility of the first differential equation of Painleve" Nagoya Math.J.117. (1990)
[文献書誌] SUWA,Tatsuo: "D-modules associated to complex analytic singular foliations"
[文献書誌] SUWA,Tatsuo: "Determinancy of complex analytic foliations germs without intergrating factors"
[文献書誌] ENDO,Sizuo: "Non-rationality of algebric tori of norm type and its application to generic division rings" Proc.Symp.Ring.theory. 22. 17-22 (1989)
[文献書誌] WATANABE,Keiichi: "Filtered rings,filtered blowing-ups and normal two-dimensional singularities with star-shaped resolution" Publ.RIMS Kyoto Univ.25. 681-740 (1989)
[文献書誌] WATANABE,Keiichi: "Regular Z-granded rings" Proc.Fac.Science,Tokai Univ.25. (1990)
[文献書誌] 宮西正宜: "代数幾何学入門" 裳華房, 350 (1990)
[文献書誌] ODA,Tadao: "Introduction to Algebraic singularities"
[文献書誌] YOSHINO,Yuji: "Theory of Cohen-Macauray modules over Hensel CM rings" Cambridge University Press,
[文献書誌] HIJIKATA,Hiroaki: "The basis problem for from on P_o(N)" American Mathematical Society(Memoris of Amer.Math.Soc.Vol.82), (1989)

1989 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 equivalence relations on algebric varieties" Journal of pure and applied algebra. 57. 83-91 (1989)

[文献書誌] MIYANISHI,Masayoshi: "Homology planes with quotient singularities" J.Math.Kyoto.Univ.

[文献書誌] MIYANISHI,Masayoshi: "Q-homology planes with C^<**>-fibrations" Osaka J.Math.

[文献書誌] ODA,Tadao: "Simple convex polytopes and the strong Lefschetz theorem" J.Pure Appl.Algebra,special issue dedicated to Professor Hideyuki Matsumura on his sixtieth birthday. (1990)

[文献書誌] ODA,Tadao: "Geometry of toric varieties" Proc.Intern.Conf.on Algebraic Groups and Applications,Univ.of Hyderabad 1989.

[文献書誌] ODA,Tadao: "Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions"

[文献書誌] MORI,Shigefumi: "Flips in families"

[文献書誌] KITAOKA,Yoshiyuki: "Forier coefficients of certain Eisenstein series" Proc.of Japan Acad.65. 253-255 (1989)

[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] MUKAI,Shigeru: "Bireqular classification of Fano threefolds and Fano manifolds of coindex 3" Proc.Nat.Acad.Sci.USA. 86. 3000-3002 (1989)

[文献書誌] YASHINO,Yuji: "Modules with Linear resolution over a polynomial ring in two variables" Nagoya Math.J.113. 89-98 (1989)

[文献書誌] HIBI,Takayuki: "What can be said about pure O-sequences?" J.Combin.Theory,Ser.A. 50. 319-322 (1989)

[文献書誌] KATSURA,Toshiyuki: "New bosonization and conformal field theory" Commun.Math.Phys.121. 603-627 (1989)

[文献書誌] TSUCHIYA,Akihiro: "Coformal field theory on moduli family of stable curves with gauge symmetries" Advanced studies in pure math.19. 459-565 (1989)

[文献書誌] KATSURA,Toshiyuki: "Formal groups and conformal field theory over Z" Advanced studies in pure math.19. 347-366 (1989)

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

[文献書誌] HIJIKATA,Hiroaki: "Orders in quaternion algebras" J.reine angew.Math.394. 59-106 (1989)

[文献書誌] MARUYAMA,Masaki: "On compactifications of moduli space of instantons"

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

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

[文献書誌] KAWAMATA,Yujiro: "Boundedness of Q-Fano threefolds"

[文献書誌] KAWAMATA,Yujiro: "Moderate degenerations of algebraic surfaces"

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

[文献書誌] FUJITA,Takao: "On adjoint bundles of ample vector bundles"

[文献書誌] SHIODA,Tetsuji: "Mordell-Weil Lattices and Galois representations I,II,III" Proc.Japan Acad.65A. 268-271,296-303 (1989)

[文献書誌] SHIODA,Tatsuji: "Construction of elliptic curves over Q(t)with high rank" Proc.Japan Acad.(1990)

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

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

[文献書誌] SUWA,Tatsuo: "D-modules associated to complex analytic singular foliations"

[文献書誌] SUWA,Tatsuo: "Determinancy of complex analytic foliations germs without intergrating factors"

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

[文献書誌] WATANABE,Keiichi: "Filtered rings,filtered blowing-ups and normal two-dimensional singularities with star-shaped resolution" Publ.RIMS Kyoto Univ.25. 681-740 (1989)

[文献書誌] WATANABE,Keiichi: "Regular Z-granded rings" Proc.Fac.Science,Tokai Univ.25. (1990)

[文献書誌] 宮西正宜: "代数幾何学入門" 裳華房, 350 (1990)

[文献書誌] ODA,Tadao: "Introduction to Algebraic singularities"

[文献書誌] YOSHINO,Yuji: "Theory of Cohen-Macauray modules over Hensel CM rings" Cambridge University Press,

[文献書誌] HIJIKATA,Hiroaki: "The basis problem for from on P_o(N)" American Mathematical Society(Memoris of Amer.Math.Soc.Vol.82), (1989)

1989 年度実績報告書

宮西正宜大阪大学, 理学部, 教授 (80025311)