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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: Melody Chan, Alberto López Martín, Nathan Pflueger and Montserrat Teixidor i Bigas
Journal: Trans. Amer. Math. Soc. 370 (2018), 3405-3439
MSC (2010): Primary 05A15, 14H51
DOI: https://doi.org/10.1090/tran/7044
Published electronically: December 27, 2017
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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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Additional Information

Melody Chan
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
Email: mtchan@math.brown.edu

Alberto López Martín
Affiliation: IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460-902, Brazil
Email: alopez@impa.br

Nathan Pflueger
Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
Address at time of publication: Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts 01002
Email: pflueger@math.brown.edu

Montserrat Teixidor i Bigas
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
Email: montserrat.teixidoribigas@tufts.edu

DOI: https://doi.org/10.1090/tran/7044
Received by editor(s): July 22, 2015
Received by editor(s) in revised form: May 31, 2016, and August 8, 2016
Published electronically: December 27, 2017
Additional Notes: The first author was supported by NSF DMS Award 1204278
The second author was supported by CAPES-Brazil
Article copyright: © Copyright 2017 American Mathematical Society

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