Mirror symmetry and the classification of orbifold del Pezzo surfaces

By M. Akhtar, Tom Coates, Alessio Corti, Liana Heuberger, Alexander M. Kasprzyk, A. Oneto, Andrea Petracci, T. Prince, Ketil Tveiten. 2015

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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 Q-Gorenstein deformation classes of del Pezzo surfaces.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8b9390749772902694a8808405077d4a57fd3a62