The rationality of the moduli space of one-pointed ineffective spin   hyperelliptic curves via an almost del Pezzo threefold
  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 $g\geq 2$. 
Hiromichi Takagi and Francesco Zucconi
math.AG