Bounds on the dimension of linear series on stable curves

Karl Christ

Published 2020-05-26Version 1

We study the dimension of linear series on stable curves. In the first part, we show that a general linear series with semistable multidegree is not special, and obtain results on the dimension of the special loci in the Picard scheme. In the process, we give a new characterization of semistability when the total degree equals the genus of the curve. In the second part, we give a generalization of Clifford's inequality to linear series of uniform multidegree and show that the new bound is achieved on every stable curve.