THE RATIONALITY OF THE MODULI SPACE OF ONE-POINTED INEFFECTIVE SPIN HYPERELLIPTIC CURVES VIA AN ALMOST DEL PEZZO THREEFOLD

Abstract

Using the geometry of an almost del Pezzo threefold, we show that the moduli space ${\mathcal{S}}_{g,1}^{0,\text{hyp}}$ of genus $g$ one-pointed ineffective spin hyperelliptic curves is rational for every $g\geqslant 2$.