CONTENT S
Abstract viii
§1 Introduction and Statement of Results 1
§2 Glossary of notation and conventions 13
§3 Gorenstein del Pezzo surfaces 15
§4 Bug-Eyed covers 20
§5 Log deformation theory 26
§6 Criteria for log uniruledness 32
§7 Reduction to 7r*lg{S°) = {1} 41
§8 Flushness and Preparation for the Hunt 44
§9 Bogomolov Bound 67
§10 Riemann Roch and Surfaces with Small Coefficient 69
§11 A partial classification of ^^-contractions 72
§12 The linear system \KS + A\ 88
§13 Classification of Bananas and Fences 92
§14 Tx a net 97
§15 g{Ax) 1 99
§16 A\ has a simple cusp 106
§17 A\ has a simple node 109
§18 Ai smooth 117
§19 The smooth banana 123
§20 Proof of (1.1) and corollaries 128
§21 A surface with 7rfg(S°) = {1} but no tiger 130
§22 Tigers, complements and toric pairs 133
§23 Classification of almost all rank one log del Pezzos 137
§L Appendix: Log terminal surface singularities and adjunction 146
§N Appendix: Normalisation of an algebraic space 149
Index to Obscure or unconventional notation 150
References 151
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