複素解析構造の総合的研究

2002 年度 実績報告書

• 研究課題/領域番号: 13304009
• 研究機関: 東京大学
• 研究代表者: 野口 潤次郎 東京大学, 大学院・数理科学研究科, 教授 (20033920)
• 研究分担者: 満渕 俊樹 大阪大学, 大学院・理学研究科, 教授 (80116102) ; 大沢 健夫 名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802) ; 藤本 坦孝 金沢大学, 理学部, 教授 (60023595) ; 宍倉 光広 京都大学, 大学院・理学研究科, 教授 (70192606) ; 風間 英明 九州大学, 大学院・数理学研究院, 教授 (10037252)
• キーワード: 多変数複素解析 / 幾何学的複素解析 / 小林双曲的多様体 / 値分布 / 擬凸領域 / モジュライ空間 / 複素力学系 / タイヒミューラー空間

研究概要

昨年度に開催された岡潔生誕百年記念多変数複素解析国際会議京都/奈良2001,で得られた成果を発表する準備をしている.そこで明らかになった諸問題を,各分担者を中心に研究が進められた.また今年度は,葉山多変数複素解析シンポジウムを開催し内外の多くの参加者を得,成果の国際的発信を行い,共同研究を行った.
代表者を中心として正則写像の値分布の研究が行われた.関数体上で準アーベル多様体のイロハ予想の類似を証明し有限性定理を得た.高次元小林双曲的射影超曲面で算術的有限性を持つものを構成した.また準アーベル多様体内の正則曲線のジェット像の構造定理を得た.山ノ井は,小関数の打ち切り個数関数を用いる第二主要定理の証明をした。藤本は,一意性多項式になる為の条件を完全に決定した.下村は,Painleve超越関数PIVについて,小関数に関する値分布を調べ,増大度の上からの評価を得ることに成功した.相原と森は共同で複素射影空間内の任意の超曲面に対して,その超曲面から定まる定数と0との間にある任意の実数を除外指数として持つ有理型写像を構成した。
大沢はL^2拡張定理を複素多様体上で証明した.清水と児玉は,非有界領域C^k×(C^*)^lの特徴付け行った.
宮嶋,赤堀らは,正規孤立特異点のモジュライに関して強擬凸CR構造の変形を通じての記述に成功した.平地は,CR幾何学および共形幾何学に現れるスカラー不変量の解析を行った.その結果,共形,CRの二つの枠組みでのQ-曲率はアンビエント計量を用いた同一の表示を持つことを示した.泊は,曲線特異点に対し多重種数δ_mを定義し、通常特異点の特徴づけを得た。
満渕は,定スカラー曲率射影代数多様体の漸近的安定性を示した.辻は,多重種数の変形不変性を劣随伴公式の形に一般化した。高山は,代数多様体上の正則直線束とその特異エルミート計量の組に対し、新しい交点理論を展開し、幾つかの基本的な結果を得た。
その他複素力学系,リーマン面のモジュライ理論,多変数正則関数空間,補間問題,ポテンシャル論での研究の進展をみた.

研究成果

• [文献書誌] J.Noguchi, J.Winkelmann: "Holomorphic curves and integral points off divisors"Math. Z.. 239. 593-610 (2002)
• [文献書誌] J.Noguchi, J.Winkelmann, K.Yamanoi: "The second main theorem for helomorphc curves into semi-Abelian varieties"Acta Math.. 188. 129-161 (2002)
• [文献書誌] J.Noguchi: "Geometric Diophantine Problems---有理点分布と値分布,「Communications in Arithmetic Fundamental Groups」"京都大学数理解析研究所講究録. 1267. 2-4 (2002)
• [文献書誌] J.Noguchi: "Some results in view of Nevanlinna theory"Number Theoretic Methods-Future Trends, China-Japan Seminar 2001. Acad Publ(To appear).
• [文献書誌] J.Noguchi: "An arithmetic property of Shirosaki's hyperbolic projective hypersurface"Forum Math.. (To appear).
• [文献書誌] 野口潤次郎: "ネヴァンリンナ理論とイロハ(abc-)予想"京都大学数理解析研究所講究録. (To appear).
• [文献書誌] J.Noguchi: "Intersection multiplicities of holomorphic and algebraic curves with divisors"Proc. OKA 100 Conference Kyoto/Nara 2001. (To appear).
• [文献書誌] Noguchi, J., Winkelmann, J.: "A note on jets of entire curves in semi-abelian varieties"Math. Z.. (To appear).
• [文献書誌] K.Fujita, M.Morimoto: "On the double series expansion of holomorphic functions"J. Math. Anal. Appl.. 272. 335-348 (2002)
• [文献書誌] K.Fujita, M.Morimoto: "Analytic functions and analytic functionals on some balls"Proceedings of the Third ISAAC Congress, Kluwer Academic Publishers. (To appear). (2002)
• [文献書誌] M.Morimoto, K.Fujita: "Holomorphic functions on the Lie ball and related topics"Proceedings of the ninth Finite or Infinite Dimensional Complex Analysis and Applications, Kluwer Academic Publisher. 33-44 (2002)
• [文献書誌] K.Fujita: "Bergman transformation for analytic functionals on some balls"Microlocal Analysis and Complex Fourier Analysis. 81-98 (2002)
• [文献書誌] S.Kamiya, J.R.Parker: "On discrete subgroups of PU(1,2 ; C) with Heisenberg translations II"Rev.Romaine Math. Pures Appl.. (To appear).
• [文献書誌] Y.Jiang, S.Kamiya, J.R.Parker: "Jorgensen's inequality for complex hyperbolic space"Geometriae Dedicata. (To appear).
• [文献書誌] S.Kamiya, J.R.Parker: "Notes on discrete subgroups of PU(1,2;C) with Heisenberg translations IV"京都大学数理解析研究所講究録. 1270. 138-144 (2002)
• [文献書誌] S.Izumi, S.Koike, T.-C.Kuo: "Computations and stability of Fukui invariant"Compositio Mathematica. 130. 49-73 (2002)
• [文献書誌] S.Izumi: "Flatness of differentiable functions along a subset of a real analytic set"Journal d'Analyse Mathematique. 86. 235-246 (2002)
• [文献書誌] S.Takayama: "Iitaka's fibrations via multiplier ideals"Trans. Amer. Math. Soc. 355. 37-47 (2003)
• [文献書誌] Masataka TOMARI: "Multiplicity of filtered rings and simple K3 singularities of multiplicity two"Publ. RIMS, Kyoto Univ.. 38. 693-724 (2002)
• [文献書誌] Masako Furuya, Masataka TOMARI: "A characterization of semi-quasihomogeneous function in terms of the Milnor number"Proc. Amer. Math. Soc.. (To appear).
• [文献書誌] M.Kato: "A Schwarz map of Appell's F_2 with projective monodromy group of order 25920"Kyushu J. Math.. (To appear).
• [文献書誌] M.Kato, M.Noumi: "Monodromy groups of hypergeometric functions satisfying algebraic equations"Tohoku Math. J.. (To appear).
• [文献書誌] Makoto Masumoto: "Algebraic relations among extremal lengths of homology classes on compact Riemann surfaces"Math. Nachr.. 239/240. 157-169 (2002)
• [文献書誌] Makoto Masumoto, Masakazu Shiba: "Hyperbolically maximal domains and fundamental domains for a discontinuous group of conformal automorphisms of a Riemann surface"Quart. J. Math. Oxford Ser. (2). 53. 337-346 (2002)
• [文献書誌] H.Tsuji: "Deformation Invariance of Plurigenra"Nagoya Math. J.. 166. 117-134 (2002)
• [文献書誌] G.Schumacher, H.Tsuji: "Quasiprojectivity of Moduli Spaces of Polarized Varieties"Annals of Mathematics. (To appear). (2003)
• [文献書誌] H.Tsuji: "Subadjunction Theorem"Proceedings of Oka 100. (To appear).
• [文献書誌] W.Bergweiler, K.Ishizaki, N.Yanagihara: "Growth of meromorphic solutions of some functional equations I"Aequationes Math.. 63. 140-151 (2002)
• [文献書誌] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients II"Tohoku Math. J.. (To appear).
• [文献書誌] K.Ishizaki: "A note on Factorization of the Weierstrass Pe-function"Proceedings of Third ISAAC Congress. (To appear).
• [文献書誌] K.Ishizaki: "A note on the functional equation f^h+g^n+h^n=1 and some complex differential equations"Computational Method and Functional Theory. (To appear).
• [文献書誌] T.Honda: "The growth theorem for k-fold symmetric convex mappings"Bulletin of the London Mathematical Society. 34. 717-724 (2002)
• [文献書誌] C.H.Chu, T.Honda: "A Schwarz lemma for bounded symmetric domains in Hilbert spaces"the Mathematical Proceedings of the Royal Irish Academy. (To appear).
• [文献書誌] M.Abe: "Meromorphic convexity of normality domains"Complex Analysis and Related Topics, Proceedings of the Japan-Korea Joint Workshop in Mathematics 2001, Yamaguchi, Japan, 22--24July 2001. 1-6 (2002)
• [文献書誌] M.Abe: "Steinness of the total space of a non-trivial algebraic affine C-bundle on the punctured complex affine plane"Mathematische Nachrichten. 238. 16-22 (2002)
• [文献書誌] M.Abe, T.Jin, T.Shima: "Remarks on universal functions of 0 C^*"Hiroshima Mathematical Journal. 33(To appear). (2003)
• [文献書誌] K.Sawada: "Picard constants of n-sheeted algebroid surfaces"Kodai Math. J.. 25 No.2. 113-138 (2002)
• [文献書誌] Y.Matsugu, S.Ueki: "Isometries of weighted Bergman-Privalov spaces on the unit ball of C^n"J. Math. Soc. Japan. 54. 341-347 (2002)
• [文献書誌] Y.Matsugu, J.Miyazawa, S.Ueki: "A characterization of weighted Bergman-Privalov spaces on the unit ball in C^n"J. Korean Math. Soc.. 39. 783-800 (2002)
• [文献書誌] (2)Y.Matsugu, J.Miyazawa: "A characterization of weighted Bergman-Orlicz spaces on the unit ball of C^n"J. Austral. Math. Soc.. 73. 1-13 (2002)
• [文献書誌] 木村秀幸: "位数p^3の非可換群の対称種数"愛知産業大学紀要. 10. 67-72 (2002)
• [文献書誌] 栗林泉, 木村秀幸: "A classification of automorphism groups up to topological equivalence of compact Riemann surface of genus 2"浜松大学経営情報学部紀要. 15. 115-123 (2002)
• [文献書誌] 木村秀幸: "閉リーマン面上の群作用が定める母関数"京都大学数理解析研究所講究録. 1270. 51-62 (2002)
• [文献書誌] S.Tajima: "Exponential polynomials and the Fourier-Borel transforms of algebraic local cohomology classes"Microlocal Analysis and Complex Fourier Analysis, eds by T.Kawai and K.Fujita, World Scientific Publishing. 284-296 (2002)
• [文献書誌] S.Tajima: "Inhomogeneous ordinaly differential equations, local cohomology and residues"Finite or infinite dimensional Complex Analysis, Hanoi. Kluwer(To appear).
• [文献書誌] Y.Nakamura, S.Tajima: "A method for constructing holonomic systems for algebraic local cohomology classes with support on a zero dimensional variety"Mathematical Software ICMS 2002, World Scientific. 158-168 (2002)
• [文献書誌] 田島慎一, 中村弥生: "代数的局所コホモロジー類の満たすホロノミック系の構成法についてII"京都大学数理解析研究所講究録. (To appear).
• [文献書誌] 田島慎一: "非同次常微分方程式の可解条件についてII"京都大学数理解析研究所講究録. (To appear).
• [文献書誌] 田島慎一: "Holonomicな定数係数線形偏微分方程式とGrothendieck duality"京都大学数理解析研究所講究録. (To appear).
• [文献書誌] S.Shimizu: "Prolongation of holomorphic vector fields on a tube domain and its applications"The Proceedings of the Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001. (To appear).
• [文献書誌] F-Y.Maeda, T.Ono: "Perturbation theory for nonlinear Dirichlet problems"Ann. Acad. Sci. Fenn.. 28(To appear). (2003)
• [文献書誌] M.Nakai, T.Tada: "The role of continuum hypothesis in the theory of harmonic dimensions"Bull. Daido Inst. Tec.. 38(To appear). (2002)
• [文献書誌] D.Partyka, K.Sakan: "On Heinz's inequality"Bull. Soc. Sci. Lettres Lodz. (To appear). (2003)
• [文献書誌] Y.Abe: "Construction of automorphic forms for ample factors of quasi-abelian varieties"Kyushu J. Math.. 57(To appear). (2003)
• [文献書誌] Y.Abe, P.Zappa: "Universal functions on Stein manifolds"J. Math. Soc. Japan. 55(To appear). (2003)
• [文献書誌] W.Bergweiler, Shunsuke Morosawa: "Semihyperbolic entire functions"Nonlinearity. 15. 1673-1684 (2002)
• [文献書誌] K.Adachi: "L^p extension of holomorphic functions from submanifolds to strictly pseudoconvex domains with non-smooth boundary"Nagoya Mathematical Journal. (To appear).
• [文献書誌] K.Kasuga: "Correction to the paper : "There are no codimension 1 linear isometries on the ball and polydisk algebras"Sci. Math. Jpn.. 56. 69-70 (2002)
• [文献書誌] Shigeki Oh'uchi: "Interpolation on countably many algebraic subsets for weighted entire functions"Osaka Journal of Mathematics. 39. 97-121 (2002)
• [文献書誌] Shun Shimomura: "On deficiencies of small functions for Painleve transcendents of the fourth kind"Ann. Acad. Sci. Fenn. Ser. A I Math.. 27. 109-120 (2002)
• [文献書誌] Shun Shimomura: "Oscillation results for n-th order linear differential equations with meromorphic periodic coefficients"Nagoya Math. J.. 166. 55-82 (2002)
• [文献書誌] Shun Shimomura: "Growth of the first, the second and the fourth Painleve transcendents"Math. Proc. Camb. Phil. Soc.. (To appear).
• [文献書誌] Shun Shimomura: "Riccati differential equations with elliptic coefficients, II"Tohoku Math. J.. (To appear).
• [文献書誌] Shun Shimomura: "Lower estimates for the growth of Painleve transcendents"Funkcial. Ekvac.. (To appear).
• [文献書誌] Shun Shimomura: "Growth of modified Painleve transcendents of the fifth and the third kind"Forum Math.. (To appear).
• [文献書誌] G.G.Gundersen, K.Tohge: "Unique range sets for polynomials or rational functions"Proceedings of the 3rd ISAAC Congress. (To appear). (2003)
• [文献書誌] K.Ishizaki, I.Laine, S.Shimomura, K.Tohge: "Riccati differential equations with elliptic coefficients, II"Tohoku Mathematical Journal. (To appear). (2003)
• [文献書誌] H.Yoshida, I.Miyamoto: "Two criterions of Wiener type for minimally thin sets and rarefied sets in a cone"J. Math. Soc. Japan. 54. 488-512 (2002)
• [文献書誌] H.Yoshida, I.Miyamoto, M.Yanagishita: "Beuring-Dahlberg-Sjogren type theorems for minimally thin sets in a cone"Canad. Math. Bull.. (To appear).
• [文献書誌] K.Matsumoto: "On the cohomological completeness of q-complete domains with corners"Nagoya Math. J.. 168. 105-112 (2002)
• [文献書誌] K.Matsumoto, T.Ohsawa: "On the real analytic Levi flat hypersurfaces in complex tori of dimension two"Ann. Inst. Fourier(Grenoble). 52. 1525-1532 (2002)
• [文献書誌] K.Matsumoto: "Levi form of logarithmic distance to complex submanifolds and its application to developability"Adv. Stud. Pure Math.. (To appear).
• [文献書誌] Yoshihiro Aihara: "Algebraic dependence of merormorphic mappings in value distribution theory"Nagoya Math. J.. 169(To appear). (2003)
• [文献書誌] Yoshihiro Aihara: "Uniqueness problem for meromorphic mappings under conditions on the preimages of divisors"Proc. of the Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001, in Advanced Studies in Pure Math.. (To appear).
• [文献書誌] H.Aikawa: "Holder continuity of the Dirichlet solution for a general domain"Bull. London Math. Soc.. 34. 691-702 (2002)
• [文献書誌] H.Aikawa, K.Hirata, T.Lund: "Martin boundary for union of convex sets"数理解析研究所講究録「ポテンシャル論とその周辺」. 1293. 1-14 (2002)
• [文献書誌] 相川弘明: "複雑領域のMartin境界と境界Harnack原理"数学. 55(To appear). (2003)
• [文献書誌] H.Aikawa, T.Lundh, T.Mizutani: "Martin boundary of a fractal domain"Potential Anal.. (To appear).
• [文献書誌] H.Aikawa: "Positive harmonic functions of finite order in a Denjoy type domain"Proc. Amer. Math. Soc.. (To appear).
• [文献書誌] A.Fujiki: "Topology of compact self-dual manifolds whose twistor space is of positive algebraic dimension"7. 587-608 (2002)
• [文献書誌] A.Fujiki: "Anti-holomorphic involutions of elliptic curves and a diffeomorphism type of certain self-dual manifolds"Lecture Note Series Math.. 7. 15-32 (2002)
• [文献書誌] A.Fujiki: "n the general fiber of an algebraic reduction of a compact complex manifolds of algebraic codimension two"J.Math. Kyoto Univ.. 42(To appear). (2002)
• [文献書誌] K.Yamanoi: "Algebro-geometric version of Nevanlinna's lemma on logarithmic derivatives and applications"Nagoya Math. J.. (To appear).
• [文献書誌] K.Yamanoi: "On Nevanlinna theory for holomorphic curves in Abelian varieties"Proceedings of the Memorial Conference of Kiyoshi Oka's Centennial Birthday on Complex Analysis in Several Variables, Kyoto/Nara 2001. (To appear).
• [文献書誌] M.Kobayashi: "Convergence of Invariant Distances on Decreasing Domains"Complex Variables Theory Appl.. 47. 155-165 (2002)
• [文献書誌] J.Kajiwara, X.D.Li, K.H.Shon: "Regeneration in Complex, Quaternionand Clifford Analysis"Finite or Infinite Dimensional Complex Analysis, Kluwer Academic Publisher(Dordrecht/Boston/London). (To appear). (2002)
• [文献書誌] J.Kajiwara, X.D.Li, K.H.Shon: "Regeneration in Quaternion Analysis"Indian Jousnal of Mathematics. (To appear). (2003)
• [文献書誌] 亀山弘, 岩井浩光, 服部晃, 竹内茂: "大学院数学教育を考える"岐阜大学教育学部研究報告(自然科学). 26-2. 1-18 (2002)
• [文献書誌] 竹内茂: "数学教育国際協力研究(2)アルゼンチン-その2"岐阜大学教育学部研究報告(自然科学). 27-1. 1-14 (2002)
• [文献書誌] Shigeru Takeuchi: "Math Ed and in/pre-service teacher training"Proc. of the ICM2002 Satellite International Conference on math education, Tibet University, Lhasa, China, August 12-17. (2002)
• [文献書誌] T.Mabuchi: "Multiplier Hermitian structures on Kahler manifolds"Nagoya Math. J.. (To appear).
• [文献書誌] A.Futaki, T.Mabuchi: "Moment maps and symmetric multilinear forms associated with symplectic classes"Asian Math. J.. 6. 349-372 (2002)
• [文献書誌] T.Mabuchi, Y.Nakagawa: "The Bando-Calabi-Futaki character as an obstruction to semistability"Math. Ann.. 324. 187-193 (2002)
• [文献書誌] T.Mabuchi: "Heat Kernel estimates and the Green functions on multiplier Hermitian manifolds"Tohoku Math. J.. 54. 259-275 (2002)
• [文献書誌] T.Mabuchi: "A theorem of Calabi-Matsushima's type"Osaka J. Math.. 39. 1-9 (2002)
• [文献書誌] H.Fujimoto: "On uniqueness polynomials for meromorphic functions"Nagoya Mathematical Journal. (To appear). (2003)
• [文献書誌] T.Umeno: "Period matrices for quasi-Abelian varieties"Japan. J. Math. 29(To appear). (2003)
• [文献書誌] T.Umeno: "On quasi-Abelian varieties over non-algebraic complex tori"Proceedings of the Sixth International Workshop on Real and Complex Analysis. (To appear). (2002)
• [文献書誌] 中川三留, 瀬川重男: "被覆面の型"数理解析研究所講究録. 1277. 84-93 (2002)
• [文献書誌] 吉永 悦男, 福井 敏純, 泉 脩藏: "特異点の数理3:解析関数と特異点"共立出版. 426 (2002)
• [文献書誌] V.I.Gromak, I.Laine, S.Shimomura: "Painleve Differential Equations in the Complex Plane"Walter de Gruyter. 303 (2002)
• [文献書誌] 相川弘明(編集): "ポテンシャル論とその周辺 講究録1293"京都大学数理解析研究所. 198 (2002)
• [文献書誌] 荷見守助, 下村勝孝: "線型代数入門"内田老鶴圃. 215 (2002)
• [文献書誌] Ohsawa, T.: "Analysis of several complex variables"Iwanami Series in Modern Mathematics. 211 (2002)