Webs of stars or how to triangulate free sums of point configurations

Abstract

A b s t r ac t . 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 partially ordered sets associated with any triangulation of a point set with one marked point, the web of stars and the stabbing poset. Triangulations of smooth Fano polytopes are discussed as a case study.