Chow classes of divisors on stacks of pointed hyperelliptic curves

TL;DR

This paper computes the classes of key divisors on stacks of pointed hyperelliptic curves, providing explicit formulas in terms of known bases, advancing the understanding of their geometric and intersection properties.

Contribution

It explicitly calculates the classes of the universal hyperelliptic Weierstrass and $g^1_2$ divisors on stacks of pointed hyperelliptic curves, expressed in terms of a known basis.

Findings

Explicit formulas for divisor classes on hyperelliptic curve stacks

Expressed results in terms of previously computed bases by Scavia

Enhances understanding of the geometry of hyperelliptic moduli spaces

Abstract

We calculate the classes of the universal hyperelliptic Weierstrass divisor $\bar{{\mathcal H}}_{g,w}$ and the universal $g^1_2$ divisor $\bar{{\mathcal H}}_{g,g^1_2}$. Our results are expressed in terms of a basis for $Cl(\bar{{\mathcal H}}_{g,1})$ and $Cl(\bar{{\mathcal H}}_{g,2})$ computed by Scavia.