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

References in corpus (9)

• Tropical varieties for non-archimedean analytic spaces
• Tropical Independence I: Shapes of Divisors and a Proof of the Gieseker-Petri Theorem
• Tropical independence II: The maximal rank conjecture for quadrics
• Brill-Noether varieties of k-gonal curves
• Special divisors on marked chains of cycles
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• The Brill-Noether rank of a tropical curve
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Cited by in corpus (2)

• Tropological Sigma Models
• The class of the Prym-Brill-Noether divisor