Cox rings of blow-ups of multiprojective spaces

IF 0.7 2区数学 Q2 MATHEMATICS

Collectanea Mathematica Pub Date : 2023-12-07 DOI:10.1007/s13348-023-00428-2

Michele Bolognesi, Alex Massarenti, Elena Poma

引用次数: 0

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 \(r\le n+2\) and for \(r = n+3\) when \(n\le 4\). 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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多射空间吹胀的考克斯环

让 \(X^{1,n}_r\) 是 \(\mathbb {P}^1\times \mathbb {P}^n\) 在 r 个一般点上的膨胀。我们描述了当 \(r\le n+2\) 和 \(r = n+3\) 时 \(X^{1,n}_r\) 的莫里锥。此外，我们还证明了 \(X^{1,n}_{n+1}\) 是 log Fano，并给出了它的考克斯环的明确表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Collectanea Mathematica 数学-数学

CiteScore

2.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.