Thomas Prince (Imperial) Smoothing del Pezzos with cyclic quotient singularities via the Gross-Siebert reconstruction algorithm
Recent work of Coates, Corti, Kaspryzk et al. aims to classify orbifold del Pezzo surfaces admitting toric degenerations using a conjectural correspondence with Laurent polynomials in two variables coming from mirror symmetry. We explain how this project lies within the Gross-Siebert program. In particular, we describe a `tropical version’ of a Q-Gorenstein smoothing and show how to apply the Gross-Siebert reconstruction algorithm to build (a formal version of) the desired toric degeneration. Given time we shall indicate how tropical disc (broken line) counts should give rise to the Laurent polynomial mirrors