Research Seminar: Complex Geometry
19.06.2015 Thomas Prince (Imperial College, London)
Smoothing del Pezzos with cyclic quotient singularities via the Gross-Siebert algorithm
Abstract:
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 expected Laurent polynomial mirrors.
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