Readership

Graduate students and research mathematicians working in algebraic geometry.

Table of Contents

• Introduction and statement of results
• Glossary of notation and conventions
• Gorenstein del Pezzo surfaces
• Bug-eyed covers
• Log deformation theory
• Criteria for log uniruledness
• Reduction to \(\pi^{\text{alg}}_{1}(S^0)=\{1\}\)
• Flushness and preparation for the hunt
• Bogomolov bound
• Riemann Roch and surfaces with small coefficient
• A partial classification of \(K_{T}\)-contractions
• the linear system \(\vert K_{S} + A\vert\)
• Classification of bananas and fences
• \(T_1\) a net
• \(g(A_1)>1\)
• \(A_1\) has a simple cusp
• \(A_1\) has a simple node
• \(A_1\) smooth
• The smooth banana
• Proof of (1.1) and corollaries
• A surface with \(\pi^{\text{alg}}_1(S^0)=\{1\}\) but no tiger
• Tigers, complements and toric pairs
• Classification of almost all rank one log del Pezzos
• Appendix: Log terminal surface singularities and adjunction
• Appendix: Normalisation of an algebraic space
• Index to obscure or unconventional notation
• References