Mirrors to Del Pezzo Surfaces and the Classification of 𝛵-Polygons

Abstract

We give a new geometric proof of the classification of 𝛵-polygons, a theorem originally due to Kasprzyk, Nill, and Prince, using ideas from mirror symmetry. In particular, this gives a completely geometric proof that any two toric ℚ-Gorenstein degenerations of a smooth del Pezzo 𝛸 surface are connected via trees of rational curves in the moduli space of 𝛸.