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Rational Curves on Quasi-Projective Surfaces
Seán Keel, University of Texas, Austin, TX, and James McKernan, University of California, Santa Barbara, CA

Memoirs of the American Mathematical Society
1999; 153 pp; softcover
Volume: 140
ISBN-10: 0-8218-1096-0
ISBN-13: 978-0-8218-1096-5
List Price: US$54
Individual Members: US$32.40
Institutional Members: US$43.20
Order Code: MEMO/140/669
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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
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