论文标题
Icosahedral Line配置和Waldschmidt常数
The icosahedral line configuration and Waldschmidt constants
论文作者
论文摘要
在$ \ mathbb {p}^2 $ 31点中有一个高度特殊的点配置，自然是由iCosahedron的几何形状引起的。 Icosahedron Projectivize $ \ Mathbb {p}^2 $的15个对称性平面，其相交点会产生31分。每个点对应于二十面体的一对顶点，面或边缘。 Icosahedron的对称组为$ G = A_5 \ times \ Mathbb {z} _2 $，这是有限的许多例外复杂反射组之一。 Icosahedron上的$ G $的动作降低到线配置上的动作上。我们在31点以研究行配置的情况下炸毁$ \ mathbb {p}^2 $。 waldschmidt常数是衡量$ \ mathbb {p}^2 $中特殊点的特殊积分的量度。在本文中，我们在此爆炸中研究了负$ g $ invariant曲线，以便计算$ 31 $奇点的理想的waldschmidt常数。
There is a highly special point configuration in $\mathbb{P}^2$ of 31 points, naturally arising from the geometry of the icosahedron. The 15 planes of symmetry of the icosahedron projectivize to 15 lines in $\mathbb{P}^2$, whose points of intersections yield the 31 points. Each point corresponds to an opposite pair of vertices, faces or edges of the icosahedron. The symmetry group of the icosahedron is $G=A_5\times \mathbb{Z}_2$, one of finitely many exceptional complex reflection groups. The action of $G$ on the icosahedron descends onto an action on the line configuration. We blow up $\mathbb{P}^2$ at the 31 points to study the line configuration. The Waldschmidt constant is a measure of how special a collection of points in $\mathbb{P}^2$. In this paper, we study negative $G$-invariant curves on this blow-up in order to compute the Waldschmidt constant of the ideal of the $31$ singularities.
