Prym-Brill-Noether Loci of special curves

Abstract

We use Young tableaux to compute the dimension of $V^r$, the Prym-Brill-Noether locus of a folded chain of loops of any gonality. This tropical result yields a new upper bound on the dimensions of algebraic Prym-Brill-Noether loci. Moreover, we prove that $V^r$ is pure-dimensional and connected in codimension $1$ when $\dim V^r\ge 1$. We then compute the first Betti number of this locus for even gonality when the dimension is exactly $1$, and compute the cardinality when the locus is finite and the edge lengths are generic.

27 pages, 10 figures. Minor revisions, to appear in IMRN