WEKO3
アイテム
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No.30\u306e\u7fa4\u306f2\u7a2e\u306e\u30e2\u30ce\u30c9\u30ed\u30df\u30fc\u7fa4\u306b\u73fe\u308c\u308b\u304c,\u305d\u3053\u3067\u306e\u53ef\u63db\u7fa4\u304c\u7570\u306a\u3063\u3066\u3044\u308b.6\u7a2e\u306e\u30e2\u30ce\u30c9\u30ed\u30df\u30fc\u7fa4\u306e\u3046\u30615\u3064\u306f4\u3064\u306e1\u6b21\u72ec\u7acb\u306a\u89e3\u306e\u9593\u306b2\u6b21\u95a2\u4fc2\u5f0f\u304c\u5b58\u5728\u3059\u308b.\u6b8b\u308a\u306e1\u3064,No.32\u306eunitary group\u3092\u3075\u304f\u3080\u30e2\u30ce\u30c9\u30ed\u30df\u30fc\u7fa4\u3092\u6301\u3064\u5fae\u5206\u65b9\u7a0b\u5f0f\u306eSchwarz map\u306e\u50cf\u306fP^3\u5185\u306e90\u6b21\u66f2\u9762\u3068\u306a\u308b\u30022)Imprimitive\u306a\u6709\u9650\u30e2\u30ce\u30c9\u30ed\u30df\u30fc\u7fa4\u3092\u3082\u3064\u3001_nF_\u003cn-1\u003e\u306e Schwarz map\u306emap\u306e\u50cfC\u306f\u65b9\u7a0b\u5f0fy^\u003cmn\u003e+xy^\u003cmq\u003e-1=0\u306e1\u6b21\u72ec\u7acb\u306an\u500b\u306e\u89e3\u306e\u6bd4\u3067\u6c7a\u307e\u308bP^\u003cn- 1\u003e\u5185\u306e\u70b9\u306e(x\u3092\u52d5\u304b\u3057\u305f\u3068\u304d\u306e)\u8ecc\u8de1\u3068\u306a\u308b.\u4e0a\u306e3\u9805n\u6b21\u65b9\u7a0b\u5f0f\u306e\u89e3\u306fx=0\u3067\u6b63\u5247\u306a\u95a2\u6570\u3067\u4e00\u822c\u578b2\u9805\u95a2\u6570\u3068\u3082\u547c\u3070\u308c\u3001\u672c\u7814\u7a76\u306b\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u3059\u3002\u7279\u306b_3F_2\u3068y^3+xy-1=0\u306e\u95a2\u4fc2\u3092\u8003\u5bdf\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u30013\u6b21\u65b9\u7a0b\u5f0f\u306e\u30ab\u30eb\u30c0\u30ce\u306e\u516c\u5f0f\u306e\u5225\u8a3c\u660e\u304c\u5f97\u3089\u308c\u308b\u3002", "subitem_description_type": "Other"}, {"subitem_description": "Appell\u0027s hypergeometric function F_2(a; b, b\u0027; c, c\u0027; x, y) =\u03a3^^\u221e_\u003cm,n=0\u003e((a,m+n)(b,m)(b\u0027,n))/((c,m)(c\u0027,n)(1,m)(1,n))x^my^n, where(a,n) = \u0393(a+n)/\u0393(a), satisfies a system E_2(a;b,b\u0027;c,c\u0027) of differential equations on the (x,y)-space X (\u3010similar or equal\u3011P^2). 1. I tabulated all the systems of parameters (a;b,b\u0027;c,c\u0027) into six classes such that each E_2(a;b,b\u0027;c,c\u0027) has a finite irreducible monodromy group. These monodromy groups have reflection subgroups whose Shephard-Todd numbers are 2,28,30 and 32. 2. The system E: = E_2(-1/\u003c12\u003e;1/6;1/\u003c12\u003e;1/3;1/2) has the biggest finite irreducible monodromy group G of order 12\u30fb25920. A Schwarz map s_E of E defined by the ratio of four linearly independent solutions of E is a 25920-valued map of X-Sing(E) into P^3, where Sing(E) denotes the singular locus of E. The closure S of the image of s_E turns out to be an irreducible hypersurface of degree 90 on which G acts.", "subitem_description_type": "Other"}, {"subitem_description": "\u7814\u7a76\u5831\u544a\u66f8", "subitem_description_type": "Other"}]}, "item_1617186643794": {"attribute_name": "Publisher", "attribute_value_mlt": [{"subitem_1522300295150": "ja", "subitem_1522300316516": "\u52a0\u85e4\u6e80\u751f"}]}, "item_1617186702042": {"attribute_name": "Language", "attribute_value_mlt": [{"subitem_1551255818386": "eng"}]}, "item_1617186783814": {"attribute_name": "Identifier", "attribute_value_mlt": [{"subitem_identifier_type": "HDL", "subitem_identifier_uri": "http://hdl.handle.net/20.500.12000/8947"}]}, "item_1617186920753": {"attribute_name": "Source Identifier", "attribute_value_mlt": [{"subitem_1522646500366": "NCID", "subitem_1522646572813": "BA6427974X"}]}, "item_1617187056579": {"attribute_name": "Bibliographic Information", "attribute_value_mlt": [{"bibliographicIssueDates": {"bibliographicIssueDate": "2002-03", "bibliographicIssueDateType": "Issued"}, "bibliographicPageStart": "none"}]}, "item_1617258105262": {"attribute_name": "Resource Type", "attribute_value_mlt": [{"resourcetype": "research report", "resourceuri": "http://purl.org/coar/resource_type/c_18ws"}]}, "item_1617265215918": {"attribute_name": "Version Type", "attribute_value_mlt": [{"subitem_1522305645492": "VoR", "subitem_1600292170262": "http://purl.org/coar/version/c_970fb48d4fbd8a85"}]}, "item_1617605131499": {"attribute_name": "File", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_access", "download_preview_message": "", "file_order": 0, "filename": "kato_m01-5.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-5.pdf"}, "version_id": "6e5451cf-c3ef-45f9-835d-a1997ffd701b"}, {"accessrole": "open_access", "download_preview_message": "", "file_order": 1, "filename": "kato_m01-4.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-4.pdf"}, "version_id": "b6a2296f-0cb7-4d45-8caf-a98c26f03792"}, {"accessrole": "open_access", "download_preview_message": "", "file_order": 2, "filename": "kato_m01-3.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-3.pdf"}, "version_id": "faa09ac9-9795-42c6-bdde-2b0aed8004f2"}, {"accessrole": "open_access", "download_preview_message": "", "file_order": 3, "filename": "kato_m01-2.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-2.pdf"}, "version_id": "3e5d9315-45ac-421b-9f63-b57393dcd39f"}, {"accessrole": "open_access", "download_preview_message": "", "file_order": 4, "filename": "kato_m01-1.pdf", "future_date_message": "", "is_thumbnail": false, "mimetype": "", "size": 0, "url": {"objectType": "fulltext", "url": "https://u-ryukyu.repo.nii.ac.jp/record/2004426/files/kato_m01-1.pdf"}, "version_id": "60d6acba-f278-4e39-8306-163a5be663cb"}]}, "item_title": "\u6709\u9650\u30e2\u30ce\u30c9\u30ed\u30df\u30fc\u7fa4\u3092\u3082\u3064\u8d85\u5e7e\u4f55\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e Schwarz map", "item_type_id": "15", "owner": "1", "path": ["1642838403123", "1642838405037"], "permalink_uri": "http://hdl.handle.net/20.500.12000/8947", "pubdate": {"attribute_name": "PubDate", "attribute_value": "2009-02-27"}, "publish_date": "2009-02-27", "publish_status": "0", "recid": "2004426", "relation": {}, "relation_version_is_last": true, "title": ["\u6709\u9650\u30e2\u30ce\u30c9\u30ed\u30df\u30fc\u7fa4\u3092\u3082\u3064\u8d85\u5e7e\u4f55\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e Schwarz map"], "weko_shared_id": -1}
有限モノドロミー群をもつ超幾何微分方程式の Schwarz map
http://hdl.handle.net/20.500.12000/8947
http://hdl.handle.net/20.500.12000/894715ed9cdf-b9ac-4a54-89d3-204c1d0af1d9
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| Item type | デフォルトアイテムタイプ（フル）(1) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 公開日 | 2009-02-27 | |||||||||
| タイトル | ||||||||||
| タイトル | 有限モノドロミー群をもつ超幾何微分方程式の Schwarz map | |||||||||
| 言語 | ja | |||||||||
| 作成者 |
加藤, 満生
× 加藤, 満生
× Kato, Mitsuo
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| アクセス権 | ||||||||||
| アクセス権 | open access | |||||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||||
| 主題 | ||||||||||
| 言語 | en | |||||||||
| 主題Scheme | Other | |||||||||
| 主題 | hypergeometric function | |||||||||
| 言語 | en | |||||||||
| 主題Scheme | Other | |||||||||
| 主題 | monodromy group | |||||||||
| 言語 | en | |||||||||
| 主題Scheme | Other | |||||||||
| 主題 | Schwarz map | |||||||||
| 内容記述 | ||||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | 科研費番号: 12640031 | |||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | 平成12年度～平成13年度 科学研究費補助金基盤研究(C)(2)研究成果報告書 / 研究概要 : Gaussの超幾何微分方程式の拡張として一般型、_<n+1>F_n, Appell型F_1,F_2,F_3,F_4,(k,n)型超幾何微分方程式等がある。本研究では,主にAppell F_2とimprimitiveな_<n+1>F_nに対して以下の研究を行った.1)有限既約なモノドロミー群をもつAppell F_2を決定した.その条件はF_2がもつ5個のパラメータによって言い表され,本質的に6種類に分類される.そのいずれの場合もモノドロミー群は簡単な可換群とunitary reflection groupとの半直積になっている.そこに現れるreflection groupはShephard-Toddの分類表のimprimitiveなG(2,2,4)とprimitiveなNo.28,30,32の群である. No.30の群は2種のモノドロミー群に現れるが,そこでの可換群が異なっている.6種のモノドロミー群のうち5つは4つの1次独立な解の間に2次関係式が存在する.残りの1つ,No.32のunitary groupをふくむモノドロミー群を持つ微分方程式のSchwarz mapの像はP^3内の90次曲面となる。2)Imprimitiveな有限モノドロミー群をもつ、_nF_<n-1>の Schwarz mapのmapの像Cは方程式y^<mn>+xy^<mq>-1=0の1次独立なn個の解の比で決まるP^<n- 1>内の点の(xを動かしたときの)軌跡となる.上の3項n次方程式の解はx=0で正則な関数で一般型2項関数とも呼ばれ、本研究に重要な役割を果す。特に_3F_2とy^3+xy-1=0の関係を考察することにより、3次方程式のカルダノの公式の別証明が得られる。 | |||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | Appell's hypergeometric function F_2(a; b, b'; c, c'; x, y) =Σ^^∞_<m,n=0>((a,m+n)(b,m)(b',n))/((c,m)(c',n)(1,m)(1,n))x^my^n, where(a,n) = Γ(a+n)/Γ(a), satisfies a system E_2(a;b,b';c,c') of differential equations on the (x,y)-space X (【similar or equal】P^2). 1. I tabulated all the systems of parameters (a;b,b';c,c') into six classes such that each E_2(a;b,b';c,c') has a finite irreducible monodromy group. These monodromy groups have reflection subgroups whose Shephard-Todd numbers are 2,28,30 and 32. 2. The system E: = E_2(-1/<12>;1/6;1/<12>;1/3;1/2) has the biggest finite irreducible monodromy group G of order 12・25920. A Schwarz map s_E of E defined by the ratio of four linearly independent solutions of E is a 25920-valued map of X-Sing(E) into P^3, where Sing(E) denotes the singular locus of E. The closure S of the image of s_E turns out to be an irreducible hypersurface of degree 90 on which G acts. | |||||||||
| 内容記述タイプ | Other | |||||||||
| 内容記述 | 研究報告書 | |||||||||
| 出版者 | ||||||||||
| 言語 | ja | |||||||||
| 出版者 | 加藤満生 | |||||||||
| 言語 | ||||||||||
| 言語 | eng | |||||||||
| 資源タイプ | ||||||||||
| 資源タイプ | research report | |||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_18ws | |||||||||
| 出版タイプ | ||||||||||
| 出版タイプ | VoR | |||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||
| 識別子 | ||||||||||
| 識別子 | http://hdl.handle.net/20.500.12000/8947 | |||||||||
| 識別子タイプ | HDL | |||||||||
| 収録物識別子 | ||||||||||
| 収録物識別子タイプ | NCID | |||||||||
| 収録物識別子 | BA6427974X | |||||||||
| 書誌情報 |
p. none, 発行日 2002-03 |
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