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.
Akhtar M., Coates T., Corti A., Heuberger L., Kasprzyk A., Oneto A., et al. (2016). Mirror symmetry and the classification of orbifold del pezzo surfaces. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 144(2), 513-527 [10.1090/proc/12876].
Mirror symmetry and the classification of orbifold del pezzo surfaces
Petracci A.;
2016
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 ℚ-Gorenstein deformation classes of del Pezzo surfaces.File in questo prodotto:
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