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. . . . . . . . . . . . . . . . . . . . . . . . . . . 10\n \n2 Preliminaries 13\n 2.1 Basic properties of weak del Pezzo surfaces . . . . . . . . . . . . . . . . . . . . 13\n 2.2 Some properties of varieties over non-closed fields . . . . . . . . . . . . . . . . . 14\n 2.3 Classes of singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15\n 2.4 Classification of weak del Pezzo surfaces . . . . . . . . . . . . . . . . . . . . . . 19\n 2.5 Basic properties of cylinders in normal projective surfaces . . . . . . . . . . . . 21\n \n3 Cylinders in weak del Pezzo fibrations 25\n 3.1 Properties of Mori conic bundles from minimal weak del Pezzo surfaces . . . . 25\n 3.2 Proof of Theorem 1.3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27\n 3.3 Proof of Theorem 1.3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33\n \n4 Cylinders in canonical del Pezzo fibrations 38\n 4.1 Du Val singularities over non-closed fields . . . . . . . . . . . . . . . . . . . . . 38\n 4.2 Proof of Theorem 1.3.9 (1) and (2) . . . . . . . . . . . . . . . . . . . . . . . . . 40\n 4.3 Properties of dvisors on weak del Pezzo surfaces . . . . . . . . . . . . . . . . . 58\n 4.4 Proof of Theorem 1.3.9 (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69\n 4.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90\n \n5 Compactifications of the affine plane over non-closed fields 93\n 5.1 Compactifications of the affine plane . . . . . . . . . . . . . . . . . . . . . . . . 93\n 5.2 Properties of twigs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94\n 5.3 Proof of Theorem 1.3.12 (1) and (2) . . . . . . . . . . . . . . . . . . . . . . . . 99\n 5.4 Proof of Theorem 1.3.12 (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102\n 5.5 Applications of Theorem 1.3.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 110\n 5.6 Remarks on Theorem 1.3.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113\n \nA Classification lists 117\n A.1 Types of weak del Pezzo surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 117\n A.2 Lc compactifications of the affine plane . . . . . . . . . . . . . . . . . . . . . . . 119\n \nReferences 124", "subitem_description_type": "Other"}]}, "item_113_description_25": {"attribute_name": "注記", "attribute_value_mlt": [{"subitem_description": "主指導教員 : 岸本崇", "subitem_description_type": "Other"}]}, "item_113_description_33": {"attribute_name": "資源タイプ", "attribute_value_mlt": [{"subitem_description": "text", "subitem_description_type": "Other"}]}, "item_113_description_34": {"attribute_name": "フォーマット", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_113_dissertation_number_19": {"attribute_name": "学位授与番号", "attribute_value_mlt": [{"subitem_dissertationnumber": "甲第1241号"}]}, "item_113_identifier_registration": {"attribute_name": "ID登録", 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Cylinders in normal surfaces over algebraically non-closed fields with an application to cylindricity of del Pezzo fibrations
https://doi.org/10.24561/00019786
https://doi.org/10.24561/00019786e0c472fb-dce8-4174-80d2-c26a1a26754f
名前 / ファイル | ライセンス | アクション |
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GD0001436.pdf (790.9 kB)
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Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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公開日 | 2023-01-26 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Cylinders in normal surfaces over algebraically non-closed fields with an application to cylindricity of del Pezzo fibrations | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_db06 | |||||
資源タイプ | doctoral thesis | |||||
ID登録 | ||||||
ID登録 | 10.24561/00019786 | |||||
ID登録タイプ | JaLC | |||||
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 | |||||
タイトル(別言語) | ||||||
その他のタイトル | 非代数閉体上に定義された曲面内のシリンダーとそのdel Pezzo ファイブレーションへの応用 | |||||
著者 |
澤原, 雅知
× 澤原, 雅知 |
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著者 ローマ字 | ||||||
SAWAHARA, Masatomo | ||||||
著者 所属 | ||||||
埼玉大学大学院理工学研究科(博士後期課程)理工学専攻 | ||||||
著者 所属(別言語) | ||||||
Graduate School of Science and Engineering, Saitama University | ||||||
書誌 | ||||||
収録物名 | 博士論文(埼玉大学大学院理工学研究科(博士後期課程)) | |||||
書誌情報 |
発行日 2022 |
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出版者名 | ||||||
出版者 | 埼玉大学大学院理工学研究科 | |||||
出版者名(別言語) | ||||||
出版者 | Graduate School of Science and Engineering, Saitama University | |||||
形態 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 127p | |||||
学位授与番号 | ||||||
学位授与番号 | 甲第1241号 | |||||
学位授与年月日 | ||||||
学位授与年月日 | 2022-03-24 | |||||
学位名 | ||||||
学位名 | 博士(理学) | |||||
学位授与機関 | ||||||
学位授与機関識別子Scheme | kakenhi | |||||
学位授与機関識別子 | 12401 | |||||
学位授与機関名 | 埼玉大学 | |||||
目次 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 1 Introduction 2 1.1 Anti-canonical polar cylinders in del Pezzo surfaces . . . . . . . . . . . . . . . . 2 1.2 Cylinders in Mori fiber spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Organization of this paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Preliminaries 13 2.1 Basic properties of weak del Pezzo surfaces . . . . . . . . . . . . . . . . . . . . 13 2.2 Some properties of varieties over non-closed fields . . . . . . . . . . . . . . . . . 14 2.3 Classes of singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4 Classification of weak del Pezzo surfaces . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Basic properties of cylinders in normal projective surfaces . . . . . . . . . . . . 21 3 Cylinders in weak del Pezzo fibrations 25 3.1 Properties of Mori conic bundles from minimal weak del Pezzo surfaces . . . . 25 3.2 Proof of Theorem 1.3.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.3 Proof of Theorem 1.3.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4 Cylinders in canonical del Pezzo fibrations 38 4.1 Du Val singularities over non-closed fields . . . . . . . . . . . . . . . . . . . . . 38 4.2 Proof of Theorem 1.3.9 (1) and (2) . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.3 Properties of dvisors on weak del Pezzo surfaces . . . . . . . . . . . . . . . . . 58 4.4 Proof of Theorem 1.3.9 (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5 Compactifications of the affine plane over non-closed fields 93 5.1 Compactifications of the affine plane . . . . . . . . . . . . . . . . . . . . . . . . 93 5.2 Properties of twigs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.3 Proof of Theorem 1.3.12 (1) and (2) . . . . . . . . . . . . . . . . . . . . . . . . 99 5.4 Proof of Theorem 1.3.12 (3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.5 Applications of Theorem 1.3.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.6 Remarks on Theorem 1.3.12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 A Classification lists 117 A.1 Types of weak del Pezzo surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 117 A.2 Lc compactifications of the affine plane . . . . . . . . . . . . . . . . . . . . . . . 119 References 124 |
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注記 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 主指導教員 : 岸本崇 | |||||
版 | ||||||
[出版社版] | ||||||
著者版フラグ | ||||||
出版タイプ | VoR | |||||
出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
資源タイプ | ||||||
内容記述タイプ | Other | |||||
内容記述 | text | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
作成日 | ||||||
日付 | 2023-01-26 | |||||
日付タイプ | Created | |||||
アイテムID | ||||||
GD0001436 |