Genera of BrillNoether curves and staircase paths in Young tableaux
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 1dimensional. Our proof uses degenerations and limit linear series along with an analysis of random staircase paths in Young tableaux, and produces an explicit schemetheoretic 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 arXiv:
 arXiv:1506.00516
 Bibcode:
 2015arXiv150600516C
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 14H51
 EPrint:
 36 pages. v2: Reorganized and improved exposition. To appear in Transactions of the AMS