1990 Fiscal Year Annual Research Report

特異点の研究

Research Project

Project/Area Number	02640024
Research Institution	Tokyo Institute of Technology
Principal Investigator	福田拓生東京工業大学, 理学部, 教授 (00009599)
Co-Investigator(Kenkyū-buntansha)	石井志保子東京工業大学, 理学部, 助教授 (60202933) 藤原大輔東京工業大学, 理学部, 教授 (10011561) 森田茂之東京工業大学, 理学部, 教授 (70011674) 藤田隆夫東京工業大学, 理学部, 教授 (40092324) 岡睦雄東京工業大学, 理学部, 教授 (40011697)
Keywords	特異点 / 完全交叉特異点 / 正規特異点 / デルペッツオ多様体 / ケ-ラ-・アインシュタイン計量 / ファインマン経路積分 / キャッソン不変量 / ビリヤ-ド問題
Research Abstract	(A)交付申請書の実施計画のIIIに挙げた特異点に関するワ-クショップはこの補助金の一部を使って開催することができた。外国人十数名日本人二十数名が参加しこじんまりしたしかし密度の濃いものになった。日本人の若い研究者に良い刺激を与えたことと、参加者の間で議論が活発に行われていくつかの共同研究の基礎ができたことは成果である。 (B)今年度の研究によって得られた新たな知見の主なものは次の通りである。各項の番号は交付申請書にあげた研究実施計画のそれに対応する。 (1)福田はコンピュ-タ実験でヒルベルトの第16問題にたいしてある予想を得た。 (2)岡は非退化完全交叉特異点に自然なストラティフィケ-ションの存在を示した。藤田は特異点のあるDel Pesso多様体の分類をほぼ完成した。石井は正規孤立特異点の多重数種の漸近的挙動に関する或法則を得た。 (5)二木はKaehlerーEinstein計量の存在に対する障害のeta不変量としての解釈を得た。藤原はFeynmanの経路積分をソボレフ空間上の広義積分としての収束を証明した。丹野はCR多様体の(1,3)型の不変量の存在およびその性質を調べた。 (7)森田はTorelli群の構造とホモロジ-3球面のCasson不変量との関連を明らかにした。 (8)盛田はある法則に従う力学系の閉軌道の分布が素数定理に従うことをしめした。志賀は位相的に有限型のリ-マン面においてHardy space H^1とBMOAの相対性を示した。

Research Products

(21 results)

All Other

All Publications (21 results)

[Publications] OKA,Mutsuo: "Canonical stratification of nonーdegenerate complete intersetion varaieties" Journal of Mathematical Society of Japan. 42. 397-422 (1990)
[Publications] OKA,Mutsuo: "Principal zetaーfunction of nonーdegenerate complete intersection variety" J.Fac.Sci.,Univ.of Tokyo. 37. 11-32 (1990)
[Publications] OKA,Mutsuo: "Toplogy of nonーdegenerate complete intersection variety" Nagoya Journal of Math.
[Publications] FUJITA,Takao: "On singular Del Pezzo Varieties" Lecture Notes in Math.Algebraic Geometry,Proc.L'Aquila 1988. 1417. 117-128 (1990)
[Publications] FUJITA,Takao: "On del Pezzo fibrations over curves" Osaka J.Math.27. 229-245 (1990)
[Publications] ISHII Shihoko: "The asymptotic behavior of pluriーgenera for a normal isolated singularity" Math.Ann.286. 803-812 (1990)
[Publications] TANNO,Shukichi: "Integral of some trigonometric functions" Kodai Math.Journal. 13. 204-209 (1990)
[Publications] TANNO,Shukichi: "Pseudoーconformal invariants of type(1.3) of CR manifolds" Hokkaido Math.Journ.
[Publications] TANNO,Shukichi: "Standard contact Riemannian structure on the unit tangent bundles," preprint.
[Publications] MORITA,Shigeyuki: "On the structure of the Torelli group and the Casson invariant" Topology,.
[Publications] MORITA,Shigeyuki: "Mapping class groups of sufaces and three dimensional manifolds" Proc.ICM 90,Kyoto.
[Publications] MORITA,Takehiko: "Symbolic representation of billiards without boundary condition" Trans.Amer.Math.Soc.
[Publications] ISHII,Shihoko: "QuasiーGorenstein Fano 3ーfolds with the isolated nonーrational loci" Composito Math.
[Publications] ISHII,Shihoko: "Simulteneous canonical models of deformations of isolated singularities" Lecture Notes in Math.,SpringerーVerlag.
[Publications] FUTAKI,AKito(with K.Tsuboi): "Eta invariants and the automorphisms of compact complex manifolds" Adv.Stud.Pure Math.(Recent Topics in Differential and Analytic Geometry). 18ーI. 251-270 (1990)
[Publications] FUTAKI,AKito(with Y.Sakane,T.Mabuchi): "EinsteinーKa^^¨hler metrics with positive Ricci curvature" ibid. 18ーI. 11-83 (1990)
[Publications] FUTAKI,AKito: "A Lie algebra character and Ka^^¨hlerーEinstein metrics of positive scalar curvature" Proc.Symp.Pure Math.,Amer.Math.Soc.
[Publications] FUJIWARA,Daisuke: "The Feynman path integral as and improper integral over the Sobolev space" Proc.of“Journe^^´e d'Equations aux derive^^´es aprtielles,Sain Jean de Mons 1990"Societe Math.de France. XIV. 1-15 (1990)
[Publications] SHIGA,Hiroshige: "Hardy spaces and BMO on Riemann surfaces"
[Publications] SHIGA,Hiroshige: "H^1ーBMO duality on Riemann surfaces"
[Publications] FUJITA,Takao: "Classification Theories of Polarized Varieties(London Math.Soc.Lecture Note Series 155)" Cambridge University Press, (1990)

1990 Fiscal Year Annual Research Report

特異点の研究

Principal Investigator

福田 拓生 東京工業大学, 理学部, 教授 (00009599)

Research Products

[Publications] OKA,Mutsuo: "Canonical stratification of nonーdegenerate complete intersetion varaieties" Journal of Mathematical Society of Japan. 42. 397-422 (1990)

[Publications] OKA,Mutsuo: "Principal zetaーfunction of nonーdegenerate complete intersection variety" J.Fac.Sci.,Univ.of Tokyo. 37. 11-32 (1990)

[Publications] OKA,Mutsuo: "Toplogy of nonーdegenerate complete intersection variety" Nagoya Journal of Math.

[Publications] FUJITA,Takao: "On singular Del Pezzo Varieties" Lecture Notes in Math.Algebraic Geometry,Proc.L'Aquila 1988. 1417. 117-128 (1990)

[Publications] FUJITA,Takao: "On del Pezzo fibrations over curves" Osaka J.Math.27. 229-245 (1990)

[Publications] ISHII Shihoko: "The asymptotic behavior of pluriーgenera for a normal isolated singularity" Math.Ann.286. 803-812 (1990)

[Publications] TANNO,Shukichi: "Integral of some trigonometric functions" Kodai Math.Journal. 13. 204-209 (1990)

[Publications] TANNO,Shukichi: "Pseudoーconformal invariants of type(1.3) of CR manifolds" Hokkaido Math.Journ.

[Publications] TANNO,Shukichi: "Standard contact Riemannian structure on the unit tangent bundles," preprint.

[Publications] MORITA,Shigeyuki: "On the structure of the Torelli group and the Casson invariant" Topology,.

[Publications] MORITA,Shigeyuki: "Mapping class groups of sufaces and three dimensional manifolds" Proc.ICM 90,Kyoto.

[Publications] MORITA,Takehiko: "Symbolic representation of billiards without boundary condition" Trans.Amer.Math.Soc.

[Publications] ISHII,Shihoko: "QuasiーGorenstein Fano 3ーfolds with the isolated nonーrational loci" Composito Math.

[Publications] ISHII,Shihoko: "Simulteneous canonical models of deformations of isolated singularities" Lecture Notes in Math.,SpringerーVerlag.

[Publications] FUTAKI,AKito(with K.Tsuboi): "Eta invariants and the automorphisms of compact complex manifolds" Adv.Stud.Pure Math.(Recent Topics in Differential and Analytic Geometry). 18ーI. 251-270 (1990)

[Publications] FUTAKI,AKito(with Y.Sakane,T.Mabuchi): "EinsteinーKa^^¨hler metrics with positive Ricci curvature" ibid. 18ーI. 11-83 (1990)

[Publications] FUTAKI,AKito: "A Lie algebra character and Ka^^¨hlerーEinstein metrics of positive scalar curvature" Proc.Symp.Pure Math.,Amer.Math.Soc.

[Publications] FUJIWARA,Daisuke: "The Feynman path integral as and improper integral over the Sobolev space" Proc.of“Journe^^´e d'Equations aux derive^^´es aprtielles,Sain Jean de Mons 1990"Societe Math.de France. XIV. 1-15 (1990)

[Publications] SHIGA,Hiroshige: "Hardy spaces and BMO on Riemann surfaces"

[Publications] SHIGA,Hiroshige: "H^1ーBMO duality on Riemann surfaces"

[Publications] FUJITA,Takao: "Classification Theories of Polarized Varieties(London Math.Soc.Lecture Note Series 155)" Cambridge University Press, (1990)

福田拓生東京工業大学, 理学部, 教授 (00009599)