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A refinement of the classical Clifford inequality

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Abstract

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

참고문헌 (16)

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