1998 Fiscal Year Annual Research Report

超平面配置の研究

Research Project

Project/Area Number	09440001
Research Institution	TOKYO METROPOLITAN UNIVERSITY
Principal Investigator	竹田雄一郎東京都立大学, 大学院・理学研究科, 助手 (30264584)
Co-Investigator(Kenkyū-buntansha)	中村博昭東京都立大学, 大学院・理学研究科, 助教授 (60217883) 蔵野和彦東京都立大学, 大学院・理学研究科, 助教授 (90205188) ト部東介東京都立大学, 大学院・理学研究科, 助教授 (70145655) 中村憲東京都立大学, 大学院・理学研究科, 教授 (80110849) 岡睦雄東京都立大学, 大学院・理学研究科, 教授 (40011697)
Keywords	超平面配置 / 超幾何積分 / 局所系コホモロジー / 鏡映群
Research Abstract	研究実績は以下の通りである。(主なものを3つ挙げる) (1) まず、鏡映群から自然に決まる超平面配置に対して、次の結果を得た。即ち、これらの超平面配置に2重に接触するベクトル場のつくる加群が自由基底を持つ。(Solmon-Teras)。この結果は、最近米国を中心に活発に研究されている。Shi型超平面配置に関するStanlet予想とも関連した著しい結果である。また、上記加群の自由基底を具体的に求めることにも成功した。自由基底の構成は齋藤微分に深く関連する。 (2) 組み合わせ的同値な超平面配置の族に対して、様々な退化が考えられるがそのGauss-Manin接続が対数的極を持つことを示した。これは、専門家の間ではある程度予想されていたが、任意の組み合わせ型をもつ超平面配置については証明されていなかった。この結果は、寺尾「超平面配置と超幾何積分」に報告されている。 (3) 鏡映面配置に極をもつ対数的微分形式を反不変微分形式の用語で特徴づけることに成功した(Shepler-Teras)ことは、不変式論の見地から対数的形式を解釈した結果である。

Research Products
(28 results)

All Other

All Publications (28 results)

[Publications] 竹田雄一郎: "On the K-groups of spherical varieties" Osaka J.Math.35. 73-81 (1998)
[Publications] 竹田雄一郎: "A relation between standard conjectures and their arithmetic aralogres" Kodai Math.J.発表予定.
[Publications] 岡睦雄: "Smooth plane curves with one place at infinity" J.Math.Soc.Japan. 49.4. 663-687 (1997)
[Publications] 岡睦雄: "Flex curves and their applications" Geometriae Dedicata. 発表予定.
[Publications] 中村憲: "Squares in binary recurrence sequences" Proceendings of the Number Theory Conference, Eger 1996. 409-421 (1998)
[Publications] 中村憲: "Recert developments of computational number theory" Number theory and its application, Kyoto 1997. 176-184 (1998)
[Publications] 青本和彦: "Connection matrices and Riemann-Hilbert problem for q-difference equations" Proc.of the 3rd Corference on Difference Equations and Its Appli, Taipei, Sept, 1997. 発表予定.
[Publications] 青本和彦: "Derivation of q-difference equation from Cannection matrix for Selberg type Jackson integrals" Jour.Difference Eq.and Its Appli. 4. 247-278 (1998)
[Publications] 青本和彦: "On elliptic product formulas for Jackson integrals associated with reduced root systems" Jour.Alg.Comb. 8. 115-126 (1998)
[Publications] 青本和彦: "On a Jacobian identity associated with real hyperplane arrangements" Composito Math. 発表予定.
[Publications] 青本和彦: "On quasi hypergeometric functions" Methods and Appli of Analysis. 発表予定.
[Publications] 青本和彦: "Singularity and monodromy of quasi hypergeometric functions" AMS Contempo.Math.発表予定.
[Publications] ト部東介: "Duality of the second Fundamental form" Real analytic and algebraic singularities. 145-148 (1998)
[Publications] 蔵野和彦: "On Macaulayfication obtained by ablow-up whose center is an equi-multiple ideal" J.of Alg.190. 405-434 (1997)
[Publications] 蔵野和彦: "The positivity of intersection multiplicities and symbolic powers of prime ideals" Compositio Math. 発表予定.
[Publications] 中村博昭: "Galois rigidity of pro-lpure braid groups an algebraic curves" Trans.Amer.Math.Soc.350. 1079-1102 (1998)
[Publications] 中村博昭: "Limits of Galois representations in fundamental groups along maximal degeneration of a lgebraic curves I" Amer.J.Math.発表予定.
[Publications] 青本和彦: "q-difference de Rham complex and Cech cohomology" Suugaku Expositions. 49 in Japanese. 350-364 (1997)
[Publications] 宮崎琢也: "The generalized Whittaker functions for Sp (2, R)" Proceedings of Japan Academy. 73. 130-133 (1977)
[Publications] 宮崎琢也: "Principal series Whittaker functions on Sp (2, R) II" Tohoku Mathematical Journal. 50. 243-260 (1998)
[Publications] 宮崎琢也: "The generalized Whittaker functions for Sp (2, R) and the gamma factor of the Andrianov's L-functions" J.of Math Sci, The Univ.of Tokyo. 発表予定.
[Publications] 寺尾宏明: "Bnbc-bases for local system cohomology on hyperplane complements" Transactions AMS. 349. 189-202 (1997)
[Publications] 寺尾宏明: "The determinant of ahypergeometric period matrix" Inventiones Math.128. 417-436 (1997)
[Publications] 寺尾宏明: "Twisted de Rham cohondogy groups of logarithmic forms" Advances in Math.128. 119-152 (1997)
[Publications] 岡睦雄: "Non-degenarate complete intensection singularity" Hermann, Paris, 309 (1997)
[Publications] 諏訪立雄: "Indices of Vector Fields and Residues of Holomorphic Foliations" Hermann, Paris, (1998)
[Publications] 石川剛郎,泉屋周一: "応用特異点論" 共立出版, (1998)
[Publications] 中居功: "Web geometry and the eqwvalence problem of 1st order partial differential equations" フランス数学会(出版予定), (1998)

1998 Fiscal Year Annual Research Report

超平面配置の研究

Principal Investigator

竹田 雄一郎 東京都立大学, 大学院・理学研究科, 助手 (30264584)

Research Products

[Publications] 竹田雄一郎: "On the K-groups of spherical varieties" Osaka J.Math.35. 73-81 (1998)

[Publications] 竹田雄一郎: "A relation between standard conjectures and their arithmetic aralogres" Kodai Math.J.発表予定.

[Publications] 岡 睦雄: "Smooth plane curves with one place at infinity" J.Math.Soc.Japan. 49.4. 663-687 (1997)

[Publications] 岡 睦雄: "Flex curves and their applications" Geometriae Dedicata. 発表予定.

[Publications] 中村 憲: "Squares in binary recurrence sequences" Proceendings of the Number Theory Conference, Eger 1996. 409-421 (1998)

[Publications] 中村 憲: "Recert developments of computational number theory" Number theory and its application, Kyoto 1997. 176-184 (1998)

[Publications] 青本和彦: "Connection matrices and Riemann-Hilbert problem for q-difference equations" Proc.of the 3rd Corference on Difference Equations and Its Appli, Taipei, Sept, 1997. 発表予定.

[Publications] 青本和彦: "Derivation of q-difference equation from Cannection matrix for Selberg type Jackson integrals" Jour.Difference Eq.and Its Appli. 4. 247-278 (1998)

[Publications] 青本和彦: "On elliptic product formulas for Jackson integrals associated with reduced root systems" Jour.Alg.Comb. 8. 115-126 (1998)

[Publications] 青本和彦: "On a Jacobian identity associated with real hyperplane arrangements" Composito Math. 発表予定.

[Publications] 青本和彦: "On quasi hypergeometric functions" Methods and Appli of Analysis. 発表予定.

[Publications] 青本和彦: "Singularity and monodromy of quasi hypergeometric functions" AMS Contempo.Math.発表予定.

[Publications] ト部東介: "Duality of the second Fundamental form" Real analytic and algebraic singularities. 145-148 (1998)

[Publications] 蔵野和彦: "On Macaulayfication obtained by ablow-up whose center is an equi-multiple ideal" J.of Alg.190. 405-434 (1997)

[Publications] 蔵野和彦: "The positivity of intersection multiplicities and symbolic powers of prime ideals" Compositio Math. 発表予定.

[Publications] 中村博昭: "Galois rigidity of pro-lpure braid groups an algebraic curves" Trans.Amer.Math.Soc.350. 1079-1102 (1998)

[Publications] 中村博昭: "Limits of Galois representations in fundamental groups along maximal degeneration of a lgebraic curves I" Amer.J.Math.発表予定.

[Publications] 青本和彦: "q-difference de Rham complex and Cech cohomology" Suugaku Expositions. 49 in Japanese. 350-364 (1997)

[Publications] 宮崎琢也: "The generalized Whittaker functions for Sp (2, R)" Proceedings of Japan Academy. 73. 130-133 (1977)

[Publications] 宮崎琢也: "Principal series Whittaker functions on Sp (2, R) II" Tohoku Mathematical Journal. 50. 243-260 (1998)

[Publications] 宮崎琢也: "The generalized Whittaker functions for Sp (2, R) and the gamma factor of the Andrianov's L-functions" J.of Math Sci, The Univ.of Tokyo. 発表予定.

[Publications] 寺尾宏明: "Bnbc-bases for local system cohomology on hyperplane complements" Transactions AMS. 349. 189-202 (1997)

[Publications] 寺尾宏明: "The determinant of ahypergeometric period matrix" Inventiones Math.128. 417-436 (1997)

[Publications] 寺尾宏明: "Twisted de Rham cohondogy groups of logarithmic forms" Advances in Math.128. 119-152 (1997)

[Publications] 岡 睦雄: "Non-degenarate complete intensection singularity" Hermann, Paris, 309 (1997)

[Publications] 諏訪立雄: "Indices of Vector Fields and Residues of Holomorphic Foliations" Hermann, Paris, (1998)

[Publications] 石川剛郎,泉屋周一: "応用特異点論" 共立出版, (1998)

[Publications] 中居功: "Web geometry and the eqwvalence problem of 1st order partial differential equations" フランス数学会(出版予定), (1998)

竹田雄一郎東京都立大学, 大学院・理学研究科, 助手 (30264584)

[Publications] 岡睦雄: "Smooth plane curves with one place at infinity" J.Math.Soc.Japan. 49.4. 663-687 (1997)

[Publications] 岡睦雄: "Flex curves and their applications" Geometriae Dedicata. 発表予定.

[Publications] 中村憲: "Squares in binary recurrence sequences" Proceendings of the Number Theory Conference, Eger 1996. 409-421 (1998)

[Publications] 中村憲: "Recert developments of computational number theory" Number theory and its application, Kyoto 1997. 176-184 (1998)

[Publications] 岡睦雄: "Non-degenarate complete intensection singularity" Hermann, Paris, 309 (1997)