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Mirror symmetry and the classification of orbifold del Pezzo surfaces


Authors: Mohammad Akhtar, Tom Coates, Alessio Corti, Liana Heuberger, Alexander Kasprzyk, Alessandro Oneto, Andrea Petracci, Thomas Prince and Ketil Tveiten
Journal: Proc. Amer. Math. Soc. 144 (2016), 513-527
MSC (2010): Primary 14S45, 52B20; Secondary 14S10, 14N35
DOI: https://doi.org/10.1090/proc/12876
Published electronically: September 24, 2015
MathSciNet review: 3430830
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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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Additional Information

Mohammad Akhtar
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: mohammad.akhtar03@imperial.ac.uk

Tom Coates
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: t.coates@imperial.ac.uk

Alessio Corti
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: a.corti@imperial.ac.uk

Liana Heuberger
Affiliation: Institut Mathematique de Jussieu, 4 Place Jussieu, 75005 Paris, France
Email: liana.heuberger@imj-prg.fr

Alexander Kasprzyk
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: a.m.kasprzyk@imperial.ac.uk

Alessandro Oneto
Affiliation: Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden
Email: oneto@math.su.se

Andrea Petracci
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: a.petracci13@imperial.ac.uk

Thomas Prince
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
Email: t.prince12@imperial.ac.uk

Ketil Tveiten
Affiliation: Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden
Email: ktveiten@math.su.se

DOI: https://doi.org/10.1090/proc/12876
Received by editor(s): January 26, 2015
Published electronically: September 24, 2015
Additional Notes: This work was supported by EPSRC grant EP/I008128/1 and ERC Starting Investigator Grant 240123.
Communicated by: Lev Borisov
Article copyright: © Copyright 2015 American Mathematical Society