Mirrors to Del Pezzo Surfaces and the Classification of $T$-Polygons

Abstract

We give a new geometric proof of the classification of $T$-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 $\mathbb{Q}$-Gorenstein degenerations of a smooth del Pezzo $X$ surface are connected via trees of rational curves in the moduli space of $X$.

References in corpus (6)

• Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces
• Homological mirror symmetry for log Calabi-Yau surfaces
• Maximally Mutable Laurent Polynomials
• Mutations of Laurent Polynomials and Flat Families with Toric Fibers
• On the geometry of anticanonical pairs
• Cluster varieties and toric specializations of Fano varieties