Cox rings of blow-ups of multiprojective spaces

Michele Bolognesi, Alex Massarenti, Elena Poma

Let $X_r^{1,n}$ be the blow-up of ${\mathbb{P}}^1\times {\mathbb{P}}^n$ in $r$ general points. We describe the Mori cone of $X_r^{1,n}$ for $r\le n+2$ and for $r=n+3$ when $n\le 4$.…