@phdthesis{oai:sucra.repo.nii.ac.jp:00019817,
 author = {澤原, 雅知},
 month = {},
 note = {127ｐ, 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, 主指導教員 : 岸本崇, text, application/pdf},
 school = {埼玉大学},
 title = {Cylinders in normal surfaces over algebraically non-closed fields with an application to cylindricity of del Pezzo fibrations},
 year = {2022},
 yomi = {サワハラ, マサトモ}
}