Prym–Brill–Noether Loci of Special Curves. (25th August 2020)

• Record Type: Journal Article
• Authors: Creech, Steven; Len, Yoav; Ritter, Caelan; Wu, Derek
• Is Part Of: International mathematics research notices. Volume 2022:Number 4(2022)
• Page Start: 2688
• Page End: 2728
• Publication Date: 2020-08-25
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa207
• Languages: English
• ISSNs: 1073-7928

Abstract

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 $\dim V^r \geq 1$ . We then compute the 1st 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.