The Integral Chow Rings of the Moduli Stacks of Hyperelliptic Prym Pairs II

Abstract: This paper is the second in a series devoted to describing the integral Chow ring of the moduli stacks $\mathcal{RH}_g$ of hyperelliptic Prym pairs. For fixed genus $g$, the stack $\mathcal{RH}_g$ is the disjoint union of $\lfloor (g+1)/2 \rfloor$ components $\mathcal{RH}_g^n$ for $n = 1, \ldots, \lfloor (g+1)/2 \rfloor$. In this paper, we compute the integral Chow rings of the components $\mathcal{RH}_g^{(g+1)/2}$ for odd $g$. Along the way, we also determine the integral Chow ring of the moduli stack of unordered pairs of two divisors in $\mathbb{P}^1$ of the same even degree.