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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Excess linear series on an algebraic curve

Authors: William Fulton, Joe Harris and Robert Lazarsfeld
Journal: Proc. Amer. Math. Soc. 92 (1984), 320-322
MSC: Primary 14H40; Secondary 14C20
MathSciNet review: 759642
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Abstract: We prove that the dimensions of the varieties $ W_d^r$ of complete linear series of degree $ d$ and dimension at least $ r$ on a curve satisfy the inequalities $ \dim W_{d - 1}^r \geqslant \dim W_d^r - (r - 1)$. In particular, a curve with $ {\infty ^2}g_d^1$'s must have a $ g_{d - 1}^1$.

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

  • [1] E. Arbarello, M. Cornalba, P. Griffiths and J. Harris, Geometry of algebraic curves, Springer-Verlag, 1984.
  • [2] Spencer Bloch and David Gieseker, The positivity of the Chern classes of an ample vector bundle, Invent. Math. 12 (1971), 112–117. MR 0297773
  • [3] William Fulton, Intersection theory, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 2, Springer-Verlag, Berlin, 1998. MR 1644323
  • [4] W. Fulton and R. Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146 (1981), no. 3-4, 271–283. MR 611386, 10.1007/BF02392466

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Article copyright: © Copyright 1984 American Mathematical Society