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

Edoardo Ballico

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

Algebraic Geometry 2013-03-04 v1

Authors: 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 $L\in {Pic}^t(C)$ with $h^0(C,L) =r+1$ . In this paper for all $g\ge 40805$ we construct several examples of smooth curves $C$ of genus $g$ with $d_3(C)/3< d_4(C)/4$ , i.e. for which a slope inequality fails.

Keywords

gonality sequence smooth curve genus quadric surface normalization singular curve slope inequality

Cite

@article{arxiv.1303.0097,
  title  = {On the gonality sequence of smooth curves: normalizations of singular curves in a quadric surface},
  author = {Edoardo Ballico},
  journal= {arXiv preprint arXiv:1303.0097},
  year   = {2013}
}

Comments

Accepted on Acta Math. Viet

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