A REFINEMENT OF THE CLASSICAL CLIFFORD INEQUALITY

Title & Authors
A REFINEMENT OF THE CLASSICAL CLIFFORD INEQUALITY
Iliev, Hristo;

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 $\small{g^r_d}$ with $\small{d{\leq}g+1}$, the inequality $\small{3r{\leq}d}$ 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 $\small{g^r_d}$ with d<3r for $\small{d{\leq}g+l,\;0{\leq}l{\leq}\frac{g}{2}-3}$, is bounded by $\small{2g-1+\frac{1}{3}(g+2l+1)}$.
Keywords
gonality;divisors;Clifford inequality;special linear series;
Language
English
Cited by
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