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arXiv · 1506.00516

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

Melody Chan·Alberto López Martín·Nathan Pflueger·Montserrat Teixidor i Bigas
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Abstract

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 when that scheme is itself a curve.

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Melody Chan, Alberto López Martín, Nathan Pflueger, Montserrat Teixidor i Bigas. 2015-06-01. Genera of Brill-Noether curves and staircase paths in Young tableaux. https://doi.org/10.1090/tran/7044

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