Mirror Symmetry for Lattice Polarized del Pezzo Surfaces
Accepted version
Peer-reviewed
Repository URI
Repository DOI
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Authors
Doran, Charles F
Thompson, Alan https://orcid.org/0000-0003-1400-0098
Abstract
We describe a notion of lattice polarization for rational elliptic surfaces and weak del Pezzo surfaces, and describe the complex moduli of the former and the K"{a}hler cone of the latter. We then propose a version of mirror symmetry relating these two objects, which should be thought of as a form of Fano-LG correspondence. Finally, we relate this notion to other forms of mirror symmetry, including Dolgachev-Nikulin-Pinkham mirror symmetry for lattice polarized K3 surfaces and the Gross-Siebert program.
Description
Keywords
math.AG, math.AG, 14J33, 14J26, 14J45, 14J28
Journal Title
Commun. Number Theory Phys. 12 (2018), no. 3, 543-580
Conference Name
Journal ISSN
1931-4523
1931-4531
1931-4531
Volume Title
12
Publisher
International Press of Boston
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/N03189X/1)