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
MathSciNet review:
3766853
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper, we compute the genus of the variety of linear series of rank and degree
on a general curve of genus
, with ramification at least
and
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