The class of the Prym-Brill-Noether divisor

2024/09/19 by Bud, Andrei
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.13034

Abstract

For r≥ 3 and g= (r(r+1))/(2), we study the Prym-Brill-Noether variety V^r(C,η) associated to Prym curves [C,η]. The locus R_g^r in R_g parametrizing Prym curves (C, η) with nonempty V^r(C,η) is a divisor. We compute some key coefficients of the class [R_g^r] in Pic_ℚ(R_g). Furthermore, we examine a strongly Brill-Noether divisor in M_g-1,2: we show its irreducibility and compute some of its coefficients in Pic_ℚ(M_g-1,2). As a consequence of our results, the moduli space R_14,2 is of general type.

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