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Rational curves on quasi-projective surfaces

About this Title

Seán Keel and James McKernan

Publication: Memoirs of the American Mathematical Society
Publication Year 1999: Volume 140, Number 669
ISBNs: 978-0-8218-1096-5 (print); 978-1-4704-0260-0 (online)
MathSciNet review: 1610249
MSC: Primary 14J26; Secondary 14B10, 14E20, 14E30

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Table of Contents


  • 1. Introduction and statement of results
  • 2. Glossary of notation and conventions
  • 3. Gorenstein del Pezzo surfaces
  • 4. Bug-eyed covers
  • 5. Log deformation theory
  • 6. Criteria for log uniruledness
  • 7. Reduction to $\pi ^{\mathrm {alg}}_1(S^0) = \{1\}$
  • 8. Flushness and preparation for the hunt
  • 9. Bogomolov bound
  • 10. Riemann Roch and surfaces with small coefficient
  • 11. A partial classification of $K_T$-contractions
  • 12. The linear system $|K_S + A|$
  • 13. Classification of bananas and fences
  • 14. $T_1$ a net
  • 15. $g(A_1) > 1$
  • 16. $A_1$ has a simple cusp
  • 17. $A_1$ has a simple node
  • 18. $A_1$ smooth
  • 19. The smooth banana
  • 20. Proof of (1.1) and corollaries
  • 21. A surface with $\pi ^{\mathrm {alg}}_1(S^0) = \{1\}$ but no tiger
  • 22. Tigers, complements and toric pairs
  • 23. Classification of all but a bounded family of rank one log del Pezzo surfaces