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Transactions of the American Mathematical Society

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Complete linear systems on rational surfaces


Author: Brian Harbourne
Journal: Trans. Amer. Math. Soc. 289 (1985), 213-226
MSC: Primary 14J26; Secondary 14C20
DOI: https://doi.org/10.1090/S0002-9947-1985-0779061-2
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] R. Hartshorne, Algebraic geometry, Springer-Verlag, Berlin and New York, 1977. MR 0463157 (57:3116)
  • [5] E. Looijenga, Rational surfaces with effective anticanonical divisor, Ann. of Math. (2) 114 (1981), 267-322. MR 632841 (83j:14030)
  • [6] Y. Manin, Cubic forms: algebra, geometry, arithmetic, North-Holland, Amsterdam, 1974. MR 833513 (87d:11037)
  • [7] M. Nagata, On rational surfaces. II, Mem. Coll. Sci. Kyoto (A) 33 (1960), 271-293. MR 0126444 (23:A3740)
  • [8] -, On the $ 14$-th problem of Hilbert, Amer. J. Math. 81 (1959), 766-772. MR 0105409 (21:4151)

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

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