A Hurwitz divisor on the moduli of Prym curves

Abstract

For even genus g = 2i ≥ 4 and the length g − 1 partition μ = (4, 2, . . . , 2,−2, . . . ,−2) of 0, we compute the first coefficients of the class of D(μ) in PicQ(Rg), where D(μ) is the divisor consisting of pairs [C, η] ∈ Rg with η = OC(2x1+x2+· · ·+xi−1−xi−· · ·−x2i−1) for some points x1, . . . , x2i−1 on C.We further provide several enumerative results that will be used for this computation.