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.References
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Additional Information
- Melody Chan
- Affiliation: Department of Mathematics, Brown University, Box 1917, Providence, Rhode Island 02912
- MR Author ID: 791839
- Email: mtchan@math.brown.edu
- Alberto López Martín
- Affiliation: IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, RJ 22460-902, Brazil
- MR Author ID: 920517
- ORCID: 0000-0002-8716-8134
- 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
- MR Author ID: 950261
- ORCID: 0000-0002-9579-9630
- Email: pflueger@math.brown.edu
- Montserrat Teixidor i Bigas
- Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
- MR Author ID: 214136
- Email: montserrat.teixidoribigas@tufts.edu
- 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 - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 3405-3439
- MSC (2010): Primary 05A15, 14H51
- DOI: https://doi.org/10.1090/tran/7044
- MathSciNet review: 3766853