2000 Fiscal Year Annual Research Report

ツイスター空間の幾何学

Research Project

Project/Area Number	12440019
Research Institution	Osaka University
Principal Investigator	藤木明大阪大学, 大学院・理学研究科, 教授 (80027383)
Co-Investigator(Kenkyū-buntansha)	小磯憲史大阪大学, 大学院・理学研究科, 教授 (70116028) 満渕俊樹大阪大学, 大学院・理学研究科, 教授 (80116102) 宮西正宜大阪大学, 大学院・理学研究科, 教授 (80025311) 後藤竜司大阪大学, 大学院・理学研究科, 助教授 (30252571) 並河良典大阪大学, 大学院・理学研究科, 助教授 (80228080)
Keywords	ツイスター空間 / 自己双対多様体 / ハイパーケーラー多様体 / 群作用 / Einstein-Weyl幾何 / モジュライ空間 / 代数次元
Research Abstract	主に,複素射影空間m個の連結和上の+型自己双対計量に対するtwistor空間を研究した. 1.代数次元はtwistor空間のもっとも基本的な不変量であるが,m≧4の場合には,代数次元2のものの存在が確立されていなかった.本研究ではJoyce twistor空間の変形としてこの様なtwistor空間を構成するとともに,その興味ある性質を見いだした.またm=4の場合にはより詳細な構造の研究が進んだ. 2.もっとも多く研究されてきたLeBrun twistor空間は,対応する自己双対空間がsemi-freeなS^1-作用を許すことで特徴づけられ,そのtwistor空間は必然的に代数次元が3となる.semifreeでないS^1-作用をゆるすtwistor空間の存在,およびその性質を問うことが基本的な問題のひとつであったが,本多はある種の退化したLeBrun twistor空間の変形として,m=4の場合にはじめて,semi-freeでないS^1-作用からくるtwistor空間を構成し,その代数次元が2になることを見いだした.さらに,代表者は,一般に,m=4,代数次元2のtwistor空間を,特にC^-作用をゆるす場合に,正則楕円fiber空間として詳細に記述した.この記述は新しい例の存在を示唆している. 3.twistor空間内の複素twistor直線の空間は,正則共形構造などの特殊な構造を持ち,これを具体的に決定することは重要であるが,今日まで組織的な研究は行われていない.本研究では,LeBrun twistor空間の場合に,この空間の構造を,その上のC^-作用をこめてほぼ決定した.さらにJoyce twistor空間の場合にも研究が進行中である.さらにhyperkahler多様体のtwistor空間の場合にも,考察を行いたい.

Research Products
(24 results)

All Other

All Publications (24 results)

[Publications] Fujiki,Akira: "Algebraic reduction of twistoe spaces of Hopf surfaces"Osaka Journal of Mathematics. 37. 847-857 (2000)
[Publications] Fujiki,Akira: "Compact self-dual manifolds with torus actions"J.of Differential Geometry. (to appear).
[Publications] Koiso,Norihito: "Convergence towards anelastica in a riemannian manifold"Osaka Journal of Mathematics. 37. 467-487 (2000)
[Publications] Koiso,Norihito: "On motions of anelastic wire and singular perturbation of a 1-dimensional plate equation"Osaka Journal of Mathematics. 37. 905-924 (2000)
[Publications] Mabuchi,Toshiki: "Kabler-Einstein metrics for manifolds with non-vanishing Futaki character"Tohoku Math.J.. (to appear).
[Publications] Mabachi,Toshiki: "Vectorfield energies and critical metrics on kahler manifolds"Nagoya Math,J.. (to appear).
[Publications] Mabuchi,Toshiki: "A Theorem of Calabi Matsusbima's type"Osak Journal of Mathematics. (to appear).
[Publications] Namikawa,Yoshinori: "Global smoothing of Calabi-Yau threefolds II"Composito Math.. (to appear).
[Publications] Namikawa,Yoshinori: "Deformation theory of singular symplectic n-folds"Mathematisches Annalen. (to appear).
[Publications] Namikawa,Yoshinori: "Extension of 2-forms and symplectic varieties"Journal for die Reire u.Angewandre Math.. (to appear).
[Publications] Honda,Nobuhiro: "A Kummer type construction of self-dual metrics on 4CP^2"J.of Math.Soc.Japan. 52. 139-160 (2000)
[Publications] Honda,Nobuhiro: "On some twistor spaces one, 4CP^2"Composito Math.. 122. 323-336 (2000)
[Publications] Honda,Nobuhiro: "Equivariant deformations of meromorphic actions on compact complex manifolds"Math.Ann.. (to appear).
[Publications] Honda,Nobuhiro: "On the structure of pedersen-Poon twistor spaces"Math.Scand.. (to appear).
[Publications] Weng,Lin: "Admissible Hermitian metricson family of line burdles over degenerating Riemann surfaces"Pacific J.Math. (to appear).
[Publications] Weng.Lin: "Ω-admissible theory II : Deligne pairings over modulo spaces of punctured Riemann surfaces."Math.Ann.. (to appear).
[Publications] Hibi,Takayuki: "Ideals with stable betti numbers"Advances in Math.. 152. 72.-77 (2000)
[Publications] Hibi,Takayuki: "Shifting operators and graded betti numbers"Journal of Algebraic Combinatorics. 12. 207-222 (2000)
[Publications] Hibi,Takayuki: "Strongly Koszul algebras"Math,.Scond. 86. 161-178 (2000)
[Publications] Miyanishi,Masayoshi: "Invariant subvarieties of low codimension"Tohoku Math.J.. 52. 11-27 (2000)
[Publications] Miyanisbi,Masayoshi: "On the Jacobian conjecture for Q-hornology planes"J.reine.angew Math.. 516. 115-132 (1999)
[Publications] Miyanishi,Masayoshi: "E'tale endomorphisms of algebraic surfaces with Gm-actions"Math.Ann. (to appear).
[Publications] Ohyama,Yousuke: "Classical solutions of Schlesinger equations and twistor theory"In Proc.of 'Iromonodromic Drformations and its appl.to physics. (to appear).
[Publications] Miyanishi,Masayoshi: "Open Algebraic Surfaces"American Mathematical Society. (2000)

2000 Fiscal Year Annual Research Report

ツイスター空間の幾何学

Principal Investigator

藤木 明 大阪大学, 大学院・理学研究科, 教授 (80027383)

Research Products

[Publications] Fujiki,Akira: "Algebraic reduction of twistoe spaces of Hopf surfaces"Osaka Journal of Mathematics. 37. 847-857 (2000)

[Publications] Fujiki,Akira: "Compact self-dual manifolds with torus actions"J.of Differential Geometry. (to appear).

[Publications] Koiso,Norihito: "Convergence towards anelastica in a riemannian manifold"Osaka Journal of Mathematics. 37. 467-487 (2000)

[Publications] Koiso,Norihito: "On motions of anelastic wire and singular perturbation of a 1-dimensional plate equation"Osaka Journal of Mathematics. 37. 905-924 (2000)

[Publications] Mabuchi,Toshiki: "Kabler-Einstein metrics for manifolds with non-vanishing Futaki character"Tohoku Math.J.. (to appear).

[Publications] Mabachi,Toshiki: "Vectorfield energies and critical metrics on kahler manifolds"Nagoya Math,J.. (to appear).

[Publications] Mabuchi,Toshiki: "A Theorem of Calabi Matsusbima's type"Osak Journal of Mathematics. (to appear).

[Publications] Namikawa,Yoshinori: "Global smoothing of Calabi-Yau threefolds II"Composito Math.. (to appear).

[Publications] Namikawa,Yoshinori: "Deformation theory of singular symplectic n-folds"Mathematisches Annalen. (to appear).

[Publications] Namikawa,Yoshinori: "Extension of 2-forms and symplectic varieties"Journal for die Reire u.Angewandre Math.. (to appear).

[Publications] Honda,Nobuhiro: "A Kummer type construction of self-dual metrics on 4CP^2"J.of Math.Soc.Japan. 52. 139-160 (2000)

[Publications] Honda,Nobuhiro: "On some twistor spaces one, 4CP^2"Composito Math.. 122. 323-336 (2000)

[Publications] Honda,Nobuhiro: "Equivariant deformations of meromorphic actions on compact complex manifolds"Math.Ann.. (to appear).

[Publications] Honda,Nobuhiro: "On the structure of pedersen-Poon twistor spaces"Math.Scand.. (to appear).

[Publications] Weng,Lin: "Admissible Hermitian metricson family of line burdles over degenerating Riemann surfaces"Pacific J.Math. (to appear).

[Publications] Weng.Lin: "Ω-admissible theory II : Deligne pairings over modulo spaces of punctured Riemann surfaces."Math.Ann.. (to appear).

[Publications] Hibi,Takayuki: "Ideals with stable betti numbers"Advances in Math.. 152. 72.-77 (2000)

[Publications] Hibi,Takayuki: "Shifting operators and graded betti numbers"Journal of Algebraic Combinatorics. 12. 207-222 (2000)

[Publications] Hibi,Takayuki: "Strongly Koszul algebras"Math,.Scond. 86. 161-178 (2000)

[Publications] Miyanishi,Masayoshi: "Invariant subvarieties of low codimension"Tohoku Math.J.. 52. 11-27 (2000)

[Publications] Miyanisbi,Masayoshi: "On the Jacobian conjecture for Q-hornology planes"J.reine.angew Math.. 516. 115-132 (1999)

[Publications] Miyanishi,Masayoshi: "E'tale endomorphisms of algebraic surfaces with Gm-actions"Math.Ann. (to appear).

[Publications] Ohyama,Yousuke: "Classical solutions of Schlesinger equations and twistor theory"In Proc.of 'Iromonodromic Drformations and its appl.to physics. (to appear).

[Publications] Miyanishi,Masayoshi: "Open Algebraic Surfaces"American Mathematical Society. (2000)

藤木明大阪大学, 大学院・理学研究科, 教授 (80027383)