2001 年度実績報告書

ツイスター空間の幾何学

研究課題

研究課題/領域番号	12440019
研究機関	大阪大学
研究代表者	藤木明大阪大学, 大学院・理学研究科, 教授 (80027383)
研究分担者	坂根由昌大阪大学, 大学院・理学研究科, 教授 (00089872) 宮西正宜大阪大学, 大学院・理学研究科, 教授 (80025311) 満渕俊樹大阪大学, 大学院・理学研究科, 教授 (80116102) 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)
キーワード	ツイスター空間 / 自己双対多様体 / 複素多様体 / 代数次元 / スカラー曲率 / 群作用 / Douady空間 / ハイパーケーラー多様体
研究概要	一般に自己双対空間のtwistor空間に関し,これに含まれる複素twistor lineのなす4次元空間の構造とその幾何学は非常に興味のある対象である.ここでは,LeBrun twistor空間と,(前年度までの研究でその基本的な構造を解明した)Joyce twistor空間について,対応するtwistor lineの空間を,その上のC^-及び(C^)^2の作用との関連をもとに詳しく研究した.特に,これらの空間をDouady空間の部分空間とみるか,Barlet空間のそれと見るかによって,興味ある差異が生ずること,境界において一般に特異性が出ることなどがわかる. 一般にLeBrun twistor空間,Joyce twistor空間には,非射影的Moishezon空間である.この非射影性に関連して,その上の群作用を用いて,それらは必ず0-homologueな正の解析的1-サイクルを含むことを証明した. LeBrun twistor空間を,C^のnon-semifreeな作用な場合に拡張することは,非常に興味ある問題である.これに関連して4P^2(射影平面4個の連結和)上の代数次元2のモデルについて,従来の研究結果をさらに補強し,その構造をより精密に決定した. Hopf曲面の右限blowing upと同相な自己双対多様体について,対応するtwistor空問の代数次元は1以下であるという代表者の予想を,C^-作用の存在の仮定もとで証明した.これは,従来のLeBrun twistor空問に対する結果を大幅に改良するものである.

研究成果
(30件)

すべてその他

すべて文献書誌 (30件)

[文献書誌] A.Fujiki: "Topology of compact self-dual manifolds whose twister space has positive algebraic dimension"Journal of Mathematical Society of Japan. 54(to appear). (2002)
[文献書誌] A.Fujiki: "Compact self-dual manifolds with torus actions"Journal of Differential Geometry. 55. 229-324 (2000)
[文献書誌] T.Mabuchi: "Vector field energies and critical metrics on K\"ahler manifolds"Nagoya Mathematical Journal. 162. 41-63 (2001)
[文献書誌] T.Mabuchi, Y.Nakagawa: "An obstruction to semistability of manifolds"Proceedings of Japan Academy. 77. 47-49 (2001)
[文献書誌] T.Mabuchi: "A theorem of Calabi-Matsushima's type"Osaka Journal of Mathematics. 39. 1-9 (2002)
[文献書誌] T.Mabuchi: "Heat Kernel estimates and the Green functions on multiplier Hermitian manifolds"Tohoku Mathematical Journal. (to appear).
[文献書誌] M.Miyanishi, K.Masuda: "Etale endomorphisms of algebraic surfaces with G_m-actions"Mathematisches Annalen. 319. 493-516 (2001)
[文献書誌] M.Miyanishi: "Completely Parametrized A^l_*-fibrations on the affine plane"Proceedings of the 8th Mathematica Society of Japan International Research Institute. (to appear).
[文献書誌] M.Miyanishi, K.Masuda: "Open algebraic surfaces with finite group actions"Transformation Groups. (to appear).
[文献書誌] Y.Namikawa: "Global smoothing of Calabi-Yau threefolds II"Composito Mathematica. 125. 55-68 (2001)
[文献書誌] Y.Namikawa: "Deformation theory of singular symplectic n-folds"Mathematisches Annalen. 319. 597-623 (2001)
[文献書誌] Y.Namikawa: "Extension of 2-forms and symplectic varieties"Journal fur die Reine und Angewandte Mathematik. 539. 123-147 (2001)
[文献書誌] Y.Namikawa: "Stratified local moduli of Calabi-Yau threefold"Topology. (to appear).
[文献書誌] Y.Namikawa: "Projectivity criterion of Moishezon spaces and density of projective sympletic varieties"International Journal of Mathematics. (to appear).
[文献書誌] Y.Namikawa: "Counter-example to global Torelli problem for irreducible simplectic manifolds"Mathematisches Annalen. (to appear).
[文献書誌] K.Takegoshi: "Strongly p-subharmonic functions and volume growth property of complete Riemannian manifolds"Osaka Journal of Mathematics. 38. 839-850 (2001)
[文献書誌] L.Weng: "Stability and New Non-Abelian Zeta Functions"Number theoretic methods-Future trends. (to appear).
[文献書誌] L.Weng: "Deligne pairings over moduli spxaces of punctured Riemann surfaces"Mathematisches Annalen. 320. 239-238 (2001)
[文献書誌] W.K.To, L.Weng: "Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces"Pacific Journal of Mathematics. 197. 441-489 (2001)
[文献書誌] Y.Ohama: "Differential equations for modular form with level three"Funkcial.Ekvac.. 44. 377-389 (2001)
[文献書誌] Y.Ohama: "Hypergemetric functions and non-associative alegebras"CRM Proceeding and Lecture Notes. 30. 173-184 (2001)
[文献書誌] Y.Ohama: "Classical Solutions of Schlesinger equations and Twistor Theory"CRM Proceeding and Lecture Notes. 31. 51-58 (2002)
[文献書誌] N.Honda: "On the structure of Pedersen-Poon twistor spaces"Mathematica Scandinavica. (to appear).
[文献書誌] N.Honda: "Degenerate double solid as twistor spaces"Communications in Analysis and Geometry. (to appear).
[文献書誌] H.Ohsugi, T.Hibi: "Convex polytopes all of whose reverse lexicographic initial ideals are squarefree"Proceedings of American Mathmatical Society. 129. 2541-2546 (2001)
[文献書誌] H.Ohsugi, T.Hibi: "Quadratic initial ideals of root systems"Proceedings of American Mathmatical Society. (to appear).
[文献書誌] A.Aramove, J.Herzog, T.Hibi: "Shellability of semigroup rings"Nagoya Mathematical Journal. (to appear).
[文献書誌] H.Ohsugi, T.Hibi: "Unimodular triangulations and coverings of configurations arising from root systems"Journal of Algebraic Combinatorics. 14. 199-219 (2001)
[文献書誌] T.Chawanya, K.Tokita: "Large dimensional replicater equations with amtisymmetric randam interactions"Journal of the Physical Society of Japan. (to appear). (2002)
[文献書誌] S.Morita, T.Chawanya: "Colletive motions inglobally coupled tent maps with stochastic"Physical Review E. (to appear). (2002)

2001 年度 実績報告書

ツイスター空間の幾何学

研究代表者

藤木 明 大阪大学, 大学院・理学研究科, 教授 (80027383)

研究成果

[文献書誌] A.Fujiki: "Topology of compact self-dual manifolds whose twister space has positive algebraic dimension"Journal of Mathematical Society of Japan. 54(to appear). (2002)

[文献書誌] A.Fujiki: "Compact self-dual manifolds with torus actions"Journal of Differential Geometry. 55. 229-324 (2000)

[文献書誌] T.Mabuchi: "Vector field energies and critical metrics on K\"ahler manifolds"Nagoya Mathematical Journal. 162. 41-63 (2001)

[文献書誌] T.Mabuchi, Y.Nakagawa: "An obstruction to semistability of manifolds"Proceedings of Japan Academy. 77. 47-49 (2001)

[文献書誌] T.Mabuchi: "A theorem of Calabi-Matsushima's type"Osaka Journal of Mathematics. 39. 1-9 (2002)

[文献書誌] T.Mabuchi: "Heat Kernel estimates and the Green functions on multiplier Hermitian manifolds"Tohoku Mathematical Journal. (to appear).

[文献書誌] M.Miyanishi, K.Masuda: "Etale endomorphisms of algebraic surfaces with G_m-actions"Mathematisches Annalen. 319. 493-516 (2001)

[文献書誌] M.Miyanishi: "Completely Parametrized A^l_*-fibrations on the affine plane"Proceedings of the 8th Mathematica Society of Japan International Research Institute. (to appear).

[文献書誌] M.Miyanishi, K.Masuda: "Open algebraic surfaces with finite group actions"Transformation Groups. (to appear).

[文献書誌] Y.Namikawa: "Global smoothing of Calabi-Yau threefolds II"Composito Mathematica. 125. 55-68 (2001)

[文献書誌] Y.Namikawa: "Deformation theory of singular symplectic n-folds"Mathematisches Annalen. 319. 597-623 (2001)

[文献書誌] Y.Namikawa: "Extension of 2-forms and symplectic varieties"Journal fur die Reine und Angewandte Mathematik. 539. 123-147 (2001)

[文献書誌] Y.Namikawa: "Stratified local moduli of Calabi-Yau threefold"Topology. (to appear).

[文献書誌] Y.Namikawa: "Projectivity criterion of Moishezon spaces and density of projective sympletic varieties"International Journal of Mathematics. (to appear).

[文献書誌] Y.Namikawa: "Counter-example to global Torelli problem for irreducible simplectic manifolds"Mathematisches Annalen. (to appear).

[文献書誌] K.Takegoshi: "Strongly p-subharmonic functions and volume growth property of complete Riemannian manifolds"Osaka Journal of Mathematics. 38. 839-850 (2001)

[文献書誌] L.Weng: "Stability and New Non-Abelian Zeta Functions"Number theoretic methods-Future trends. (to appear).

[文献書誌] L.Weng: "Deligne pairings over moduli spxaces of punctured Riemann surfaces"Mathematisches Annalen. 320. 239-238 (2001)

[文献書誌] W.K.To, L.Weng: "Admissible Hermitian metrics on families of line bundles over certain degenerating Riemann surfaces"Pacific Journal of Mathematics. 197. 441-489 (2001)

[文献書誌] Y.Ohama: "Differential equations for modular form with level three"Funkcial.Ekvac.. 44. 377-389 (2001)

[文献書誌] Y.Ohama: "Hypergemetric functions and non-associative alegebras"CRM Proceeding and Lecture Notes. 30. 173-184 (2001)

[文献書誌] Y.Ohama: "Classical Solutions of Schlesinger equations and Twistor Theory"CRM Proceeding and Lecture Notes. 31. 51-58 (2002)

[文献書誌] N.Honda: "On the structure of Pedersen-Poon twistor spaces"Mathematica Scandinavica. (to appear).

[文献書誌] N.Honda: "Degenerate double solid as twistor spaces"Communications in Analysis and Geometry. (to appear).

[文献書誌] H.Ohsugi, T.Hibi: "Convex polytopes all of whose reverse lexicographic initial ideals are squarefree"Proceedings of American Mathmatical Society. 129. 2541-2546 (2001)

[文献書誌] H.Ohsugi, T.Hibi: "Quadratic initial ideals of root systems"Proceedings of American Mathmatical Society. (to appear).

[文献書誌] A.Aramove, J.Herzog, T.Hibi: "Shellability of semigroup rings"Nagoya Mathematical Journal. (to appear).

[文献書誌] H.Ohsugi, T.Hibi: "Unimodular triangulations and coverings of configurations arising from root systems"Journal of Algebraic Combinatorics. 14. 199-219 (2001)

[文献書誌] T.Chawanya, K.Tokita: "Large dimensional replicater equations with amtisymmetric randam interactions"Journal of the Physical Society of Japan. (to appear). (2002)

[文献書誌] S.Morita, T.Chawanya: "Colletive motions inglobally coupled tent maps with stochastic"Physical Review E. (to appear). (2002)

2001 年度実績報告書

藤木明大阪大学, 大学院・理学研究科, 教授 (80027383)