论文标题
Cox的cox圈环和复曲面旗束
Cox rings of projectivized toric vector bundles and toric flag Bundles
论文作者
论文摘要
冈萨雷斯（González），赫林（Hering），佩恩（Payne）和苏斯（Süss）的作品表明，可以在投影式的摩尔武器矢量捆绑中找到莫里梦境的示例和非例子。这个结果，以及项目活动的圆环矢量束的数据的组合性质使它们成为问题的理想测试类：是什么使多样性成为莫里梦想的空间？在本文中，我们考虑了关于矢量束的自然代数操作的这个问题。 假设$ \ Mathcal {e} $是一个折叠的向量捆绑包，使得projectivization $ \ m athbb {p} \ mathcal {e} $是一个梦dream以求的空间，那么直接总和是什么时候捆绑$ \ mathbb {p}（p}（p}（\ mathcal {\ mathcal {e} \ oplus \ oplus \ mathcal \ nathcalcalcalcalcalcalcalcal {e}） $ \ mathbb {p}（\ Mathcal {e} \ oplus \ Mathcal {e} \ oplus \ oplus \ Mathcal \ Mathcal {e}）\ ldots $也是Mori Dream Spaces吗？我们通过与关联的完整标志束$ \ Mathcal {fl}（\ Mathcal {e}）$的关系给出了这个问题的答案。我们描述了几类示例，并为整个旗杆捆绑包的Cox环计算了一个演示文稿。
Work of González, Hering, Payne, and Süss shows that it is possible to find both examples and non-examples of Mori dream spaces among projectivized toric vector bundles. This result, and the combinatorial nature of the data of projectivized toric vector bundles make them an ideal test class for the question: what makes a variety a Mori dream space? In the present paper we consider this question with respect to natural algebraic operations on vector bundles. Suppose $\mathcal{E}$ is a toric vector bundle such that the projectivization $\mathbb{P}\mathcal{E}$ is a Mori dream space, then when are the direct sum bundles $\mathbb{P}(\mathcal{E} \oplus \mathcal{E})$, $\mathbb{P}(\mathcal{E} \oplus \mathcal{E} \oplus \mathcal{E})\ldots$ also Mori dream spaces? We give an answer to this question utilizing a relationship with the associated full flag bundle $\mathcal{FL}(\mathcal{E})$. We describe several classes of examples, and we compute a presentation for the Cox ring of the full flag bundle for the tangent bundle of projective space.
