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

Chan, Melody; López Martín, Alberto; Pflueger, Nathan; Teixidor i Bigas, Montserrat

doi:10.1090/tran/7044

Genera of Brill-Noether curves and staircase paths in Young tableaux
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by Melody Chan, Alberto López Martín, Nathan Pflueger and Montserrat Teixidor i Bigas PDF

Trans. Amer. Math. Soc. 370 (2018), 3405-3439 Request permission

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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