Invariants of the Brill-Noether curve

2014/03/28 by Castorena, Abel, Martín, Alberto López, Bigas, Montserrat Teixidor i · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1403.7489

Abstract

For a projective nonsingular curve of genus g, the Brill-Noether locus W^r_d(C) parametrizes line bundles of degree d over C with at least r+1 sections. When the curve is generic and the Brill-Noether number ρ(g,r,d) equals 1, one can then talk of the Brill-Noether curve. In this paper, we explore the first two invariants of this curve, giving a new way of calculating the genus of this curve and computing its gonality when C has genus 5.

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• Continuous Linear Series

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