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Transactions of the American Mathematical Society

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



Anticanonical Rational Surfaces

Author: Brian Harbourne
Journal: Trans. Amer. Math. Soc. 349 (1997), 1191-1208
MSC (1991): Primary 14C20, 14J26; Secondary 14M20, 14N05
MathSciNet review: 1373636
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Abstract: 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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Brian Harbourne
Affiliation: Department of Mathematics and Statistics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0323

Keywords: Anticanonical, rational, surface, base points, fixed components, linear systems
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.
Article copyright: © Copyright 1997 American Mathematical Society