Research & Notes

Project: Triangulations of Convex Lattice Polygons

In this project, led by Elizabeth Gasparim, we develop an algorithm that computes all triangulations for a given polygon arising from representations of toric varieties. We also discuss the possible smooth configurations most likely to precede the singularity. Code for triangulation, internal edge classification, and visualisation is hosted in the polytope-triangulations repository.

One possible "universal quilt" assembled from all 79 triangulations corresponding to the crepant resolutions of the Calabi-Yau threefold singularity C³/(Z₃ × Z₃).