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Transactions of the American Mathematical Society

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

 

 

Complete linear systems on rational surfaces


Author: Brian Harbourne
Journal: Trans. Amer. Math. Soc. 289 (1985), 213-226
MSC: Primary 14J26; Secondary 14C20
MathSciNet review: 779061
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Abstract: We determine the dimension, fixed components and base points of complete linear systems on blowings-up of $ {{\mathbf{P}}^2}$ having irreducible anticanonical divisor.


References [Enhancements On Off] (What's this?)

  • [1] M. Demazure, Surfaces de Del Pezzo, Lecture Notes in Math., Vol. 777, Springer-Verlag, Berlin and New York, 1980, pp. 23-69.
  • [2] P. DuVal, On the Kantor group of a set of points in a plane, Proc. London Math. Soc. 42 (1937), 18-51.
  • [3] B. Harbourne, Moduli of rational surfaces, Ph.D. Thesis, M.I.T., 1982.
  • [4] Robin Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977. Graduate Texts in Mathematics, No. 52. MR 0463157
  • [5] Eduard Looijenga, Rational surfaces with an anticanonical cycle, Ann. of Math. (2) 114 (1981), no. 2, 267–322. MR 632841, 10.2307/1971295
  • [6] 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
  • [7] Masayoshi Nagata, On rational surfaces. II, Mem. Coll. Sci. Univ. Kyoto Ser. A Math. 33 (1960/1961), 271–293. MR 0126444
  • [8] Masayoshi Nagata, On the 14-th problem of Hilbert, Amer. J. Math. 81 (1959), 766–772. MR 0105409

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DOI: https://doi.org/10.1090/S0002-9947-1985-0779061-2
Article copyright: © Copyright 1985 American Mathematical Society