论文标题
$ \ mathbb {p}^3 $的Cox Cox戒指的离散几何形状
Discrete geometry of Cox rings of blow-ups of $\mathbb{P}^3$
论文作者
论文摘要
我们证明了$ \ mathbb {p}^3 $ $ 7 $点的Cox Ring的理想的二次发电，以解决Lesieutre和Park的猜想。为此，我们计算了Khovanskii基础，实施了在Del Pezzo表面的情况下实现成功的技术。这样的基础使我们对相关的多面体编码相对于所有投影嵌入的曲折变性的复合品种进行了退化。我们研究了这些多面体的边缘图，并介绍了Mukai Edge图。
We prove quadratic generation for the ideal of the Cox ring of the blow-up of $\mathbb{P}^3$ at $7$ points, solving a conjecture of Lesieutre and Park. To do this we compute Khovanskii bases, implementing techniques which proved successful in the case of Del Pezzo surfaces. Such bases give us degenerations to toric varieties whose associated polytopes encode toric degenerations with respect to all projective embeddings. We study the edge-graphs of these polytopes and we introduce the Mukai edge graph.
