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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Anticanonical Rational Surfaces
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by Brian Harbourne PDF
Trans. Amer. Math. Soc. 349 (1997), 1191-1208 Request permission


A determination of the fixed components, base points and irregularity is made for arbitrary numerically effective divisors on any smooth projective rational surface having an effective anticanonical divisor. All of the results are proven over an algebraically closed field of arbitrary characteristic. Applications, to be treated in separate papers, include questions involving: points in good position, birational models of rational surfaces in projective space, and resolutions for 0-dimensional subschemes of $\mathbf {P}^{2}$ defined by complete ideals.
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Additional Information
  • Brian Harbourne
  • Affiliation: Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0323
  • MR Author ID: 217048
  • Email:
  • Received by editor(s): September 29, 1995
  • Additional Notes: This work was supported both by the National Science Foundation and by a Spring 1994 University of Nebraska Faculty Development Leave. I would also like to thank Tony Geramita for a helpful discussion, and the referee for a careful reading of the paper.
  • © Copyright 1997 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 349 (1997), 1191-1208
  • MSC (1991): Primary 14C20, 14J26; Secondary 14M20, 14N05
  • DOI:
  • MathSciNet review: 1373636