Rational Picard group of moduli of pointed hyperelliptic curves

TL;DR

This paper computes the rational divisor class group of moduli spaces of smooth pointed hyperelliptic curves and their compactifications over the complex numbers, advancing understanding of their geometric structure.

Contribution

It provides the first explicit determination of the rational Picard group for these moduli spaces and their compactifications.

Findings

Rational divisor class group of moduli spaces determined

Results apply to both smooth and compactified hyperelliptic curves

Enhances understanding of the geometry of hyperelliptic moduli spaces

Abstract

We determine the rational divisor class group of the moduli spaces of smooth pointed hyperelliptic curves and of their Deligne-Mumford compactification, over the field of complex numbers.