# Genera of Brill-Noether curves and staircase paths in Young tableaux

@article{Chan2015GeneraOB,
title={Genera of Brill-Noether curves and staircase paths in Young tableaux},
author={M. Chan and A. Mart'in and Nathan Pflueger and M. Bigas},
journal={arXiv: Algebraic Geometry},
year={2015}
}
• M. Chan, +1 author M. Bigas
• Published 2015
• Mathematics
• arXiv: Algebraic Geometry
• In this paper, we compute the genus of the variety of linear series of rank $r$ and degree $d$ on a general curve of genus $g$, with ramification at least $\alpha$ and $\beta$ at two given points, when that variety is 1-dimensional. Our proof uses degenerations and limit linear series along with an analysis of random staircase paths in Young tableaux, and produces an explicit scheme-theoretic description of the limit linear series of fixed rank and degree on a generic chain of elliptic curves… CONTINUE READING