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arXiv · 2308.11283

Cox rings of blow-ups of multiprojective spaces

Michele Bolognesi·Alex Massarenti·Elena Poma
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Abstract

Let $X^{1,n}_r$ be the blow-up of $\mathbb{P}^1\times\mathbb{P}^n$ in $r$ general points. We describe the Mori cone of $X^{1,n}_r$ for $r\leq n+2$ and for $r = n+3$ when $n\leq 4$. Furthermore, we prove that $X^{1,n}_{n+1}$ is log Fano and give an explicit presentation for its Cox ring.

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Michele Bolognesi, Alex Massarenti, Elena Poma. 2023-08-22. Cox rings of blow-ups of multiprojective spaces. https://arxiv.org/abs/2308.11283

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