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

TL;DR

This paper computes the integral Chow rings of specific moduli stacks of Prym pairs, focusing on cases with Weierstrass points and certain pairs for odd genus curves, advancing understanding of their algebraic structure.

Contribution

It provides the first explicit calculations of the Chow rings for these Prym moduli stacks, covering cases with Weierstrass points and particular pair configurations for odd genus.

Findings

Chow ring for Prym pairs from a single Weierstrass point computed.

Chow ring for Prym pairs with up to (g-1)/2 pairs for odd g determined.

New algebraic relations in the Chow rings established.

Abstract

This paper is the first in a series dedicated to computing the integral Chow rings of the moduli stacks of Prym pairs. In this work, we compute the Chow ring for Prym pairs arising from a single pair of Weierstrass points and from at most $(g-1)/2 $ pairs when the genus $g$ of the curve is odd.