The rationality of the moduli space of one-pointed ineffective spin hyperelliptic curves via an almost del Pezzo threefold

TL;DR

This paper proves that the moduli space of genus g one-pointed ineffective spin hyperelliptic curves is rational for all g ≥ 2 by leveraging the geometry of an almost del Pezzo threefold.

Contribution

It establishes the rationality of the moduli space for all g ≥ 2 using geometric methods involving an almost del Pezzo threefold, a novel approach in this context.

Findings

The moduli space is rational for all g ≥ 2.

The approach uses the geometry of an almost del Pezzo threefold.

The result applies to one-pointed ineffective spin hyperelliptic curves.

Abstract

Using the geometry of an almost del Pezzo threefold, we show that the moduli space of genus $g$ one-pointed ineffective spin hyperelliptic curves is rational for every $g\geq 2$.