Prym–Brill–Noether Loci of Special Curves. (25th August 2020) - Creech, Steven; Len, Yoav; Ritter, Caelan; Wu, Derek
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 V^r ≥ 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.