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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 .

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Complete linear systems on rational surfaces
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by Brian Harbourne PDF
Trans. Amer. Math. Soc. 289 (1985), 213-226 Request permission


We determine the dimension, fixed components and base points of complete linear systems on blowings-up of ${{\mathbf {P}}^2}$ having irreducible anticanonical divisor.
    M. Demazure, Surfaces de Del Pezzo, Lecture Notes in Math., Vol. 777, Springer-Verlag, Berlin and New York, 1980, pp. 23-69. P. DuVal, On the Kantor group of a set of points in a plane, Proc. London Math. Soc. 42 (1937), 18-51. B. Harbourne, Moduli of rational surfaces, Ph.D. Thesis, M.I.T., 1982.
  • Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York-Heidelberg, 1977. MR 0463157
  • Eduard Looijenga, Rational surfaces with an anticanonical cycle, Ann. of Math. (2) 114 (1981), no. 2, 267–322. MR 632841, DOI 10.2307/1971295
  • Yu. I. Manin, Cubic forms, 2nd ed., North-Holland Mathematical Library, vol. 4, North-Holland Publishing Co., Amsterdam, 1986. Algebra, geometry, arithmetic; Translated from the Russian by M. Hazewinkel. MR 833513
  • Masayoshi Nagata, On rational surfaces. II, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 33 (1960/61), 271–293. MR 126444, DOI 10.1215/kjm/1250775912
  • Masayoshi Nagata, On the $14$-th problem of Hilbert, Amer. J. Math. 81 (1959), 766–772. MR 105409, DOI 10.2307/2372927
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 289 (1985), 213-226
  • MSC: Primary 14J26; Secondary 14C20
  • DOI:
  • MathSciNet review: 779061