Delaunay triangulations of lens spaces
Abstract
Description
We compute the convex hull in $\mathbb{C}^2$ of an arbitrary finite subgroup of ${\mathbb{C}^*}^2$. The combinatorics are dictated by continued fractions in a natural way. This reproves a theorem of Smilansky, with a slightly stronger intermediary step.
16 pages, no figures. This second version mentions reference [S2], where the main result was already proved, and is extended to achieve the same level of generality as [S2]. Our key step (Claim 12) is slightly stronger than in [S2]
16 pages, no figures. This second version mentions reference [S2], where the main result was already proved, and is extended to achieve the same level of generality as [S2]. Our key step (Claim 12) is slightly stronger than in [S2]