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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)
DOI: https://doi.org/10.1090/memo/0669
MathSciNet review: 1610249
MSC: Primary 14J26; Secondary 14B10, 14E20, 14E30
Table of Contents
Chapters
- 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