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={Melody Chan and Alberto L'opez Mart'in and Nathan Pflueger and Montserrat Teixidor I. Bigas},
  journal={arXiv: Algebraic Geometry},
  year={2015}
}
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… Expand

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