| 概要 | Many spaces of interest in algebraic geometry have covering spaces which are complements of hyperplane arrangements in various spaces. We study the metric-space completion of the universal cover of such a hyperplane complement. We show that under a certain local condition on the arrangement, the universal cover is contractible. We conjecture that this condition holds for the arrangement of a finite Coxeter group, and show that this conjecture implies the contractibility of (for example) the universal covers of the discriminant complements of all of Arnol'd's unimodal singularities. |