Mirror symmetry and the classification of orbifold del Pezzo surfaces

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

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.

Citation

Akhtar, M., Coates, T., Corti, A., Heuberger, L., Kasprzyk, A. M., Oneto, A., Petracci, A., Prince, T., & Tveiten, K. (2016). Mirror symmetry and the classification of orbifold del Pezzo surfaces. Proceedings of the American Mathematical Society, 144(2), 513-527. https://doi.org/10.1090/proc/12876

• Journal Article Type: Article
• Publication Date: Feb 1, 2016
• Deposit Date: Dec 14, 2015
• Publicly Available Date: Feb 1, 2016
• Journal: Proceedings of the American Mathematical Society
• Print ISSN: 0002-9939
• Electronic ISSN: 1088-6826
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 144
• Issue: 2
• Pages: 513-527
• DOI: https://doi.org/10.1090/proc/12876
• Public URL: https://nottingham-repository.worktribe.com/output/978198
• Publisher URL: http://dx.doi.org/10.1090/proc/12876
• Related Public URLs: http://www.ams.org/publications/journals/journalsframework/proc
• Additional Information: First published in Proceedings of the American Mathematical Society in v. 144, no. 2, published by the American Mathematical Society.