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 $X$.
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