Mirror symmetry and the classification of orbifold del Pezzo surfaces

Akhtar, Mohammad; Coates, Tom; Corti, Alessio; Heuberger, Liana; Kasprzyk, Alexander; Oneto, Alessandro; Petracci, Andrea; Prince, Thomas; Tveiten, Ketil

doi:10.1090/proc/12876

Mirror symmetry and the classification of orbifold del Pezzo surfaces
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by Mohammad Akhtar, Tom Coates, Alessio Corti, Liana Heuberger, Alexander Kasprzyk, Alessandro Oneto, Andrea Petracci, Thomas Prince and Ketil Tveiten

Proc. Amer. Math. Soc. 144 (2016), 513-527

DOI: https://doi.org/10.1090/proc/12876

Published electronically: September 24, 2015

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Abstract:

We state a number of conjectures that together allow one to classify a broad class of del Pezzo surfaces with cyclic quotient singularities using mirror symmetry. We prove our conjectures in the simplest cases. The conjectures relate mutation-equivalence classes of Fano polygons with $\mathbb {Q}$-Gorenstein deformation classes of del Pezzo surfaces.

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