1989 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)	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)
Keywords	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
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。

Research Products
(37 results)

All Other

All Publications (37 results)

[Publications] MIYANISHI,Masayoshi: "Finite equivalence relations on algebric varieties" Journal of pure and applied algebra. 57. 83-91 (1989)
[Publications] MIYANISHI,Masayoshi: "Homology planes with quotient singularities" J.Math.Kyoto.Univ.
[Publications] MIYANISHI,Masayoshi: "Q-homology planes with C^<**>-fibrations" Osaka J.Math.
[Publications] 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)
[Publications] ODA,Tadao: "Geometry of toric varieties" Proc.Intern.Conf.on Algebraic Groups and Applications,Univ.of Hyderabad 1989.
[Publications] ODA,Tadao: "Linear Gale transforms and Gelfand-Kapranov-Zelevinskij decompositions"
[Publications] MORI,Shigefumi: "Flips in families"
[Publications] KITAOKA,Yoshiyuki: "Forier coefficients of certain Eisenstein series" Proc.of Japan Acad.65. 253-255 (1989)
[Publications] KITAOKA,Yoshiyuki: "Some remarks on representations of positive definite quadratic forms" Nagoya Math.J.115. 23-41 (1989)
[Publications] MUKAI,Shigeru: "Bireqular classification of Fano threefolds and Fano manifolds of coindex 3" Proc.Nat.Acad.Sci.USA. 86. 3000-3002 (1989)
[Publications] YASHINO,Yuji: "Modules with Linear resolution over a polynomial ring in two variables" Nagoya Math.J.113. 89-98 (1989)
[Publications] HIBI,Takayuki: "What can be said about pure O-sequences?" J.Combin.Theory,Ser.A. 50. 319-322 (1989)
[Publications] KATSURA,Toshiyuki: "New bosonization and conformal field theory" Commun.Math.Phys.121. 603-627 (1989)
[Publications] TSUCHIYA,Akihiro: "Coformal field theory on moduli family of stable curves with gauge symmetries" Advanced studies in pure math.19. 459-565 (1989)
[Publications] KATSURA,Toshiyuki: "Formal groups and conformal field theory over Z" Advanced studies in pure math.19. 347-366 (1989)
[Publications] NAGATA,Masayoshi: "Some remarks on the two-dimensional Jacobian Conjecture" Chinese Journ.of Math.17. 1-7 (1989)
[Publications] HIJIKATA,Hiroaki: "Orders in quaternion algebras" J.reine angew.Math.394. 59-106 (1989)
[Publications] MARUYAMA,Masaki: "On compactifications of moduli space of instantons"
[Publications] MARUYAMA,Masaki: "Limits of instantons"
[Publications] KAWAMATA,Yujiro: "Small contractions of four dimensional algebraic maniforlds" Math.Ann.284. 595-600 (1989)
[Publications] KAWAMATA,Yujiro: "Boundedness of Q-Fano threefolds"
[Publications] KAWAMATA,Yujiro: "Moderate degenerations of algebraic surfaces"
[Publications] FUJITA,Takao: "On Del Pezzo fibrations over curves" Osaka J.Math.27. (1990)
[Publications] FUJITA,Takao: "On adjoint bundles of ample vector bundles"
[Publications] SHIODA,Tetsuji: "Mordell-Weil Lattices and Galois representations I,II,III" Proc.Japan Acad.65A. 268-271,296-303 (1989)
[Publications] SHIODA,Tatsuji: "Construction of elliptic curves over Q(t)with high rank" Proc.Japan Acad.(1990)
[Publications] SUMIHIRO,Hideyasu: "On the geometry of determinantal varieties associated to 2-bundles on P^n"
[Publications] UMEMURA,Hiroshi: "Second proof of the irreducibility of the first differential equation of Painleve" Nagoya Math.J.117. (1990)
[Publications] SUWA,Tatsuo: "D-modules associated to complex analytic singular foliations"
[Publications] SUWA,Tatsuo: "Determinancy of complex analytic foliations germs without intergrating factors"
[Publications] 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)
[Publications] WATANABE,Keiichi: "Filtered rings,filtered blowing-ups and normal two-dimensional singularities with star-shaped resolution" Publ.RIMS Kyoto Univ.25. 681-740 (1989)
[Publications] WATANABE,Keiichi: "Regular Z-granded rings" Proc.Fac.Science,Tokai Univ.25. (1990)
[Publications] 宮西正宜: "代数幾何学入門" 裳華房, 350 (1990)
[Publications] ODA,Tadao: "Introduction to Algebraic singularities"
[Publications] YOSHINO,Yuji: "Theory of Cohen-Macauray modules over Hensel CM rings" Cambridge University Press,
[Publications] HIJIKATA,Hiroaki: "The basis problem for from on P_o(N)" American Mathematical Society(Memoris of Amer.Math.Soc.Vol.82), (1989)

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

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

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

[Publications] 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)

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

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

[Publications] MORI,Shigefumi: "Flips in families"

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

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

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

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

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

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

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

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

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

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

[Publications] MARUYAMA,Masaki: "On compactifications of moduli space of instantons"

[Publications] MARUYAMA,Masaki: "Limits of instantons"

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

[Publications] KAWAMATA,Yujiro: "Boundedness of Q-Fano threefolds"

[Publications] KAWAMATA,Yujiro: "Moderate degenerations of algebraic surfaces"

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

[Publications] FUJITA,Takao: "On adjoint bundles of ample vector bundles"

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

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

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

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

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

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

[Publications] 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)

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

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

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

[Publications] ODA,Tadao: "Introduction to Algebraic singularities"

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

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

宮西正宜大阪大学, 理学部, 教授 (80025311)