Rational curves on quasi-projective surfaces / [electronic resource] Se�an Keel, James McKernan.

By: Keel, Se�anContributor(s): McKernan, James, 1964-Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v. 669Publication details: Providence, R.I. : American Mathematical Society, c1999Description: 1 online resource (viii, 153 p. : ill.)ISBN: 9781470402600 (online)Subject(s): Surfaces, Algebraic | Algebraic varietiesAdditional physical formats: Rational curves on quasi-projective surfaces /DDC classification: 510 s | 516.3/52 LOC classification: QA3 | .A57 no. 669 | QA573Online resources: Contents | Contents
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
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"July 1999, volume 140, number 669 (third of 4 numbers)."

Includes bibliographical references (p. 151-153) and index.

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

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

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