1993 Fiscal Year Annual Research Report

多様体に関する諸問題

Research Project

Project/Area Number	05452001
Research Institution	Tohoku University
Principal Investigator	小田忠雄東北大学, 理学部, 教授 (60022555)
Co-Investigator(Kenkyū-buntansha)	石田正典東北大学, 理学部, 助教授 (30124548) 西川青季東北大学, 理学部, 教授 (60004488) 森田康夫東北大学, 理学部, 教授 (20011653) 砂田利一東北大学, 理学部, 教授 (20022741) 堀田良之東北大学, 理学部, 教授 (70028190)
Keywords	トーリック多様体 / モーデル・ヴェイユ群 / 一般ヤコビ多様体 / 有理点 / ヤン・バックスター方程式 / 調和写像 / スペクトル幾何 / アインシュタイン計量
Research Abstract	1.代数幾何学的側面からは,トーリック多様体のドラーム・コホモロジーや交差コホモロジーの完全に代数的な記述に成功し,また,準楕円曲面のモーデル・ヴェイユ群や一般ヤコビ多様体のコンパクト化につき新知見を得た. 2.数論的側面からは,代数体上の代数多様体の有理点を考察し,有理点を持つ線織面の構成および不分岐被覆との関連に関し新知見を得た. 3.代数解析的側面および数理物理的側面からは,同変D加群の基礎付けおよびヤン・バックスター方程式の楕円関数解に関する新知見を得た. 4.大域解析学,微分幾何学および複素幾何学的側面からは,双曲空間内の非有界凸多面体間の調和写像,スペクトル幾何,アインシュタイン計量に関する多くの新知見を得た. 5.上記の諸成果の大部分は,いろいろの側面からの異なった視点の持ち寄りとそれらの総合化によって初めて可能となった. 6.これまでに得られている関連知見をデータベースにより極めて高能率に検索できた. 7.研究成果の受信・発信を活発に行なった.

Research Products

(18 results)

All Other

All Publications (18 results)

[Publications] Tadao Oda: "The algebraic de Rham theorem for toric varieties." Tohoku Math.J.45. 231-247 (1993)
[Publications] Ryoshi Hotta: "Equivariant D-modules." Proc.ICPAM Wuhan Spring School,Hermann,Paris. (出版予定).
[Publications] Seiki Nishikawa(K.Akutagawa): "Harmonic maps between unbounded convex polyhedra in hyperbolic spaces." Invent.Math.(出版予定).
[Publications] Toshikazu Sunada(T.Adachi): "The densities of states in spectral geometry." Comment.Math.Helvetici. 68. 480-493 (1993)
[Publications] Toshikazu Sunada: "A discrete analogue of periodic magnetic Schrodinger operators." Contemporary Math.(出版予定).
[Publications] Toshikazu Sunada: "Magnetic flows on a Riemann surface." Proc.of KAIST Symposium. (出版予定).
[Publications] Shin Nayatani(S.Kato): "Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold." Nagoya Math.J.132. 155-173 (1993)
[Publications] Koji Hasegawa: "Crossing symmetry in elliptic solution of the Yang-Baxter equation and a new L operator for Belavin's solution." J.Physics,A:Math.Gen.26. 3211-3228 (1993)
[Publications] Hiroyuki Ito: "The Mordell-Weil groups of unirational quasi-elliptic surfaces in characteristic 2." Tohoku Math.J.46(出版予定). (1994)
[Publications] Yasuhiro Nakagawa: "Einstein-Kahler toric Fano fourfolds." Tohoku Math.J.45. 297-310 (1993)
[Publications] Yasuhiro Nakagawa: "Classification of Einstein-Kahler toric Fano fourfolds." Tohoku Math.J.46. 125-133 (1994)
[Publications] Takeshi Kajiwara: "Logarithmic compactifications of the generalized Jacobian variety." J.Fac.Sci.Univ.Tokyo,Sect.IA,Math.40. 473-502 (1993)
[Publications] Toshikazu Sunada: "Euclidean versus non-Euclidean aspects in spectral geometry." Progress in Theoretical Physics. (出版予定).
[Publications] Shigetoshi Bando: "Einstein-Hermitian metrics on open Kahler manifolds." Lecture Notes in Pure and Appl.Math.,Marcel Dekker. 27-33 (1993)
[Publications] Hiraku Nakajima: "Monopoles and Nahm's equations." Lecture Notes in Pure and Appl.Math.,Marcel Dekker. 193-211 (1993)
[Publications] Hiraku Nakajima: "Homology of moduli spaces of instantons on ALE spaces(1)" J.Dirrerential Geom.(出版予定).
[Publications] Hiraku Nakajima: "Gauge theory on resolutions of simple singularities and simple Lie algebras." International Math.Research Notes. (出版予定).
[Publications] Shin Nayatani: "Morse index and Gauss maps of complete minimal surfaces in Euclidean 3-space." Comment.Math.Helvetici. 68. 511-537 (1993)

1993 Fiscal Year Annual Research Report

多様体に関する諸問題

Principal Investigator

小田 忠雄 東北大学, 理学部, 教授 (60022555)

Research Products

[Publications] Tadao Oda: "The algebraic de Rham theorem for toric varieties." Tohoku Math.J.45. 231-247 (1993)

[Publications] Ryoshi Hotta: "Equivariant D-modules." Proc.ICPAM Wuhan Spring School,Hermann,Paris. (出版予定).

[Publications] Seiki Nishikawa(K.Akutagawa): "Harmonic maps between unbounded convex polyhedra in hyperbolic spaces." Invent.Math.(出版予定).

[Publications] Toshikazu Sunada(T.Adachi): "The densities of states in spectral geometry." Comment.Math.Helvetici. 68. 480-493 (1993)

[Publications] Toshikazu Sunada: "A discrete analogue of periodic magnetic Schrodinger operators." Contemporary Math.(出版予定).

[Publications] Toshikazu Sunada: "Magnetic flows on a Riemann surface." Proc.of KAIST Symposium. (出版予定).

[Publications] Shin Nayatani(S.Kato): "Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold." Nagoya Math.J.132. 155-173 (1993)

[Publications] Koji Hasegawa: "Crossing symmetry in elliptic solution of the Yang-Baxter equation and a new L operator for Belavin's solution." J.Physics,A:Math.Gen.26. 3211-3228 (1993)

[Publications] Hiroyuki Ito: "The Mordell-Weil groups of unirational quasi-elliptic surfaces in characteristic 2." Tohoku Math.J.46(出版予定). (1994)

[Publications] Yasuhiro Nakagawa: "Einstein-Kahler toric Fano fourfolds." Tohoku Math.J.45. 297-310 (1993)

[Publications] Yasuhiro Nakagawa: "Classification of Einstein-Kahler toric Fano fourfolds." Tohoku Math.J.46. 125-133 (1994)

[Publications] Takeshi Kajiwara: "Logarithmic compactifications of the generalized Jacobian variety." J.Fac.Sci.Univ.Tokyo,Sect.IA,Math.40. 473-502 (1993)

[Publications] Toshikazu Sunada: "Euclidean versus non-Euclidean aspects in spectral geometry." Progress in Theoretical Physics. (出版予定).

[Publications] Shigetoshi Bando: "Einstein-Hermitian metrics on open Kahler manifolds." Lecture Notes in Pure and Appl.Math.,Marcel Dekker. 27-33 (1993)

[Publications] Hiraku Nakajima: "Monopoles and Nahm's equations." Lecture Notes in Pure and Appl.Math.,Marcel Dekker. 193-211 (1993)

[Publications] Hiraku Nakajima: "Homology of moduli spaces of instantons on ALE spaces(1)" J.Dirrerential Geom.(出版予定).

[Publications] Hiraku Nakajima: "Gauge theory on resolutions of simple singularities and simple Lie algebras." International Math.Research Notes. (出版予定).

[Publications] Shin Nayatani: "Morse index and Gauss maps of complete minimal surfaces in Euclidean 3-space." Comment.Math.Helvetici. 68. 511-537 (1993)

小田忠雄東北大学, 理学部, 教授 (60022555)