{"created":"2023-05-15T15:29:55.392120+00:00","id":19817,"links":{},"metadata":{"_buckets":{"deposit":"290d75b5-3192-4525-92b0-c02de9510f8e"},"_deposit":{"created_by":3,"id":"19817","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"19817"},"status":"published"},"_oai":{"id":"oai:sucra.repo.nii.ac.jp:00019817","sets":["94:429:431:432:1037"]},"author_link":["30653"],"control_number":"19817","item_113_alternative_title_1":{"attribute_name":"タイトル（別言語）","attribute_value_mlt":[{"subitem_alternative_title":"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"}]},"item_113_biblio_info_9":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2022","bibliographicIssueDateType":"Issued"}}]},"item_113_date_35":{"attribute_name":"作成日","attribute_value_mlt":[{"subitem_date_issued_datetime":"2023-01-26","subitem_date_issued_type":"Created"}]},"item_113_date_granted_20":{"attribute_name":"学位授与年月日","attribute_value_mlt":[{"subitem_dategranted":"2022-03-24"}]},"item_113_degree_grantor_22":{"attribute_name":"学位授与機関","attribute_value_mlt":[{"subitem_degreegrantor":[{"subitem_degreegrantor_name":"埼玉大学"}],"subitem_degreegrantor_identifier":[{"subitem_degreegrantor_identifier_name":"12401","subitem_degreegrantor_identifier_scheme":"kakenhi"}]}]},"item_113_degree_name_21":{"attribute_name":"学位名","attribute_value_mlt":[{"subitem_degreename":"博士(理学)"}]},"item_113_description_13":{"attribute_name":"形態","attribute_value_mlt":[{"subitem_description":"127ｐ","subitem_description_type":"Other"}]},"item_113_description_24":{"attribute_name":"目次","attribute_value_mlt":[{"subitem_description":"1 Introduction 2\n  1.1 Anti-canonical polar cylinders in del Pezzo surfaces . . . . . . . . . . . . . . . . 2\n  1.2 Cylinders in Mori fiber spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4\n  1.3 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5\n  1.4 Organization of this paper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24561/00019786","subitem_identifier_reg_type":"JaLC"}]},"item_113_publisher_11":{"attribute_name":"出版者名","attribute_value_mlt":[{"subitem_publisher":"埼玉大学大学院理工学研究科"}]},"item_113_publisher_12":{"attribute_name":"出版者名（別言語）","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Science and Engineering, Saitama 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