Acta Mathematica Vietnamica

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On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface
Edoardo Ballico

 

Abstract

Let C be a smooth curve of genus g. For each positive integer r, the r-gonality d r (C) of C is the minimal integer t such that there is LPict (C)   with h0(C,L)=r+1. In this paper, for all g≥40805 we construct several examples of smooth curves C of genus g with d3(C)/3<d4(C)/4, i.e. for which a slope inequality fails.

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