Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A REFINEMENT OF THE CLASSICAL CLIFFORD INEQUALITY

  • Iliev, Hristo (DEPARTMENT OF MATHEMATICS SEOUL NATIONAL UNIVERSITY)
  • Published : 2007.05.31
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Abstract

We offer a refinement of the classical Clifford inequality about special linear series on smooth irreducible complex curves. Namely, we prove about curves of genus g and odd gonality at least 5 that for any linear series $g^r_d$ with $d{\leq}g+1$, the inequality $3r{\leq}d$ holds, except in a few sporadic cases. Further, we show that the dimension of the set of curves in the moduli space for which there exists a linear series $g^r_d$ with d<3r for $d{\leq}g+l,\;0{\leq}l{\leq}\frac{g}{2}-3$, is bounded by $2g-1+\frac{1}{3}(g+2l+1)$.

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