2002 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)	並河良典大阪大学, 大学院・理学研究科, 助教授 (80228080) 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) 本多宣博広島大学, 大学院・理学研究科, 助手 (60311809) 後藤竜司大阪大学, 大学院・理学研究科, 助教授 (30252571)
Keywords	ツイスター空間 / 自己双対多様体 / 複素多様体 / 代数次元
Research Abstract	1.(M, g)を+型の自己双対多様体で(S^1×S^3)#mP^2,m≧0,と同相であるとする.(ただしS^kはk次元球面,#は連結和,mP^2は複素射影平面m個の連結和を表す.)いまMのツイスター空間が既約実二次因子でM上分岐するものを含むとする.このときMは必然的に(S^1×S^3)#mP^2と微分同相になる.これはMが単連結の場合のPedersen-Poonの結果の拡張であるが,この場合には,非特異楕円曲線上の反正則対合的自己同型とその固定点の集合の形状を求めることが問題になる. 2.(M, g)をコンパクト連結自己双対多様体としZをこれに同伴なツイスター空間とする.a)Zの代数次元a(Z)が2であるとすると,1)MはmP^2と同相であるか,2)Mのある有限次不分岐被覆が(S^1×S^3)#mP^2と同相になる.b)a(Z)が1で(M, g)が+型であるとすると,Mの1次元ベッチ数は0または1で,前者の場合は上のa)が,後者の場合は上のb)または代数リダクションの一般ファイバーが大域的球殻を含まないb_2>0のVII型の曲面になる.ただし上述のようなVII型曲面は非存在が予想されており最後の場合は起こらないと考えられる.kの結果によりツイスター空間の代数次元が正である自己双対多様体は強い位相敵制限を受けることがわかった. 3.代数余次元が2であるコンパクト複素多様体Zに対しその代数リダクションをあたえるファイバー空間をf : Z→Yとする.このときいfの一般ファイバーは決して,種数の2以上の線織面とはならない.しかるに種数1の線織面はそのようなファイバーとして現れうる.これは従前信じられていた結果の一部の誤りを正し,残りの部分の正しい証明を与えるものである.

Research Products
(17 results)

All Other

All Publications (17 results)

[Publications] A.Fujiki: "On the general fiber of an algebraic reduction of a compact complex manifold of algebraic codimension two"J.Math.Kyoto Univ.. 42・4(In press). (2002)
[Publications] A.Fujiki: "Anti-holomorphic involution of elliptic curve and a diffeomorphism type of certain self-dual manifolds"Lecture Notes Series in Math.. 7. 15-32 (2002)
[Publications] A.Fujiki: "Topology of compact self-dual manifolds whose twistor space is of positive dimension"J.Math.Soc.Japan. 54・3. 587-608 (2002)
[Publications] Y.Namikawa: "Mukai flops and derived categories"J.Reine.Angew.Math.. (To appear).
[Publications] Y.Namikawa: "Counter-example to global Torelli problem for irreducible symplectic manifolds"Math.Ann.. 324. 841-845 (2002)
[Publications] Y.Namikawa: "Stratified local moduli of Calabi-Yau threefolds"Topology. 41. 1219-1237 (2002)
[Publications] Y.Namikawa: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International Journal of Math.. 13. 125-135 (2002)
[Publications] Y.Namikawa: "Calabi-Yau threefolds and deformation theory"Sugaku Exposition. 15. 1-29 (2002)
[Publications] K.Masuda, M.Miyanishi: "The additive group actions on Q-homology planes"Annales de l'Institut Fourier. (To appear).
[Publications] M.Miyanishi, De-Qi Zhang: "Equivariant classification of Gorenstein open log del Pezzo surfaces with finite group actions"J.Math.Soc.Japan. (To appear).
[Publications] K.Masuda, M.Miyanishi: "Open algebraic surfaces with finite group actions"Transformation Groups. 7. 185-207 (2002)
[Publications] N.Koiso: "Vortex filament equation in a riemannian manifold"Tohoku Math.J.. (To appear).
[Publications] Y.Ohyama: "Classical Solutions of Schlesinger equations and Twistor Theory"CRM Proceedings and Lecture Notes. 31. 51-58 (2002)
[Publications] T.Mabuchi: "Multiplier Hermitian structures on K"ahler manifolds"Nagoya J.Math.. (To appear).
[Publications] A.Futaki, T.Mabuchi: "Moment maps and symmetric multilinear forms associated with symplectic classes"Asian Math.J.. (To appear).
[Publications] T.Mabuchi, Y.Nakagawa: "The Band-Calabi-Futaki character as an obstruction to semistability"Math.Ann.. (To appear).
[Publications] T.Mabuchi: "Heat Kernel estimates and the Green functions on multiplier Hermitian manifolds"Tohoku Math.J.. 54(In press). (2002)

2002 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] A.Fujiki: "On the general fiber of an algebraic reduction of a compact complex manifold of algebraic codimension two"J.Math.Kyoto Univ.. 42・4(In press). (2002)

[Publications] A.Fujiki: "Anti-holomorphic involution of elliptic curve and a diffeomorphism type of certain self-dual manifolds"Lecture Notes Series in Math.. 7. 15-32 (2002)

[Publications] A.Fujiki: "Topology of compact self-dual manifolds whose twistor space is of positive dimension"J.Math.Soc.Japan. 54・3. 587-608 (2002)

[Publications] Y.Namikawa: "Mukai flops and derived categories"J.Reine.Angew.Math.. (To appear).

[Publications] Y.Namikawa: "Counter-example to global Torelli problem for irreducible symplectic manifolds"Math.Ann.. 324. 841-845 (2002)

[Publications] Y.Namikawa: "Stratified local moduli of Calabi-Yau threefolds"Topology. 41. 1219-1237 (2002)

[Publications] Y.Namikawa: "Projectivity criterion of Moishezon spaces and density of projective symplectic varieties"International Journal of Math.. 13. 125-135 (2002)

[Publications] Y.Namikawa: "Calabi-Yau threefolds and deformation theory"Sugaku Exposition. 15. 1-29 (2002)

[Publications] K.Masuda, M.Miyanishi: "The additive group actions on Q-homology planes"Annales de l'Institut Fourier. (To appear).

[Publications] M.Miyanishi, De-Qi Zhang: "Equivariant classification of Gorenstein open log del Pezzo surfaces with finite group actions"J.Math.Soc.Japan. (To appear).

[Publications] K.Masuda, M.Miyanishi: "Open algebraic surfaces with finite group actions"Transformation Groups. 7. 185-207 (2002)

[Publications] N.Koiso: "Vortex filament equation in a riemannian manifold"Tohoku Math.J.. (To appear).

[Publications] Y.Ohyama: "Classical Solutions of Schlesinger equations and Twistor Theory"CRM Proceedings and Lecture Notes. 31. 51-58 (2002)

[Publications] T.Mabuchi: "Multiplier Hermitian structures on K"ahler manifolds"Nagoya J.Math.. (To appear).

[Publications] A.Futaki, T.Mabuchi: "Moment maps and symmetric multilinear forms associated with symplectic classes"Asian Math.J.. (To appear).

[Publications] T.Mabuchi, Y.Nakagawa: "The Band-Calabi-Futaki character as an obstruction to semistability"Math.Ann.. (To appear).

[Publications] T.Mabuchi: "Heat Kernel estimates and the Green functions on multiplier Hermitian manifolds"Tohoku Math.J.. 54(In press). (2002)

藤木明大阪大学, 大学院・理学研究科, 教授 (80027383)