标题： Waldschmidt常数的对称点集在$\mathbb{P}^3$ 显示英文标题

标题： Waldschmidt constants of symmetric sets of points in $\mathbb{P}^3$

摘要： 由复反射群定义的点配置近年来在多个研究方向上引起了广泛关注，例如理想普通幂与符号幂之间的包含问题、意外超曲面理论、研究一般投影为完全交的点集以及围绕有界负性猜想的思想。 为了更好地理解这些配置，已经进行了多次尝试来计算它们的各种不变量。 本文我们关注它们的Waldschmidt常数。 在由反射群确定的平面点配置的情况下，大多数（但不是全部）Waldschmidt常数已经被知晓。 在这里，我们转向$\mathbb{P}^3$中的配置，由于除子与曲线之间的对应关系不再可用，因此需要新的思路。 特别是，我们精确计算了来自$D_4,B_4,F_4$和$H_4$根系的$\mathbb{P}^3$中点配置的Waldschmidt常数。 显示英文摘要

摘要： Configurations of points defined by complex reflection groups have attracted a lot of attention recently in several directions of research, e.g., the containment problem between ordinary and symbolic powers of ideals, in the theory of unexpected hypersurfaces, in the study of sets of points whose general projections are complete intersections and in the ideas revolving around the Bounded Negativity Conjecture. In order to understand these configurations better several attempts have been undertaken to compute their various invariants. In this paper we focus on their Waldschmidt constants. In the case of plane configurations of points determined by reflection groups most (but not all) Waldschmidt constants are known. Here we pass to configurations in $\mathbb{P}^3$ where new ideas are required as the identification between divisors and curves is no longer available. In particular, we precisely compute the Waldschmidt constant for configurations of points in $\mathbb{P}^3$ coming from the $D_4,B_4,F_4$, and $H_4$ root systems.