Webs of stars or how to triangulate free sums of point configurations
arXiv:1512.08411 · doi:10.1016/j.jcta.2018.05.007
Abstract
The triangulations of point configurations which decompose as a free sum are classified in terms of the triangulations of the summands. The methods employ two new kinds of partially ordered sets to be associated with any triangulation of a point set with one point marked, the "web of stars" and the "stabbing poset". Triangulations of smooth Fano polytopes are discussed as a case study.
29 pages, 13 figures