English

Mirror Symmetry for Lattice Polarized del Pezzo Surfaces

Algebraic Geometry 2018-09-28 v2

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.

Keywords

Cite

@article{arxiv.1709.00856,
  title  = {Mirror Symmetry for Lattice Polarized del Pezzo Surfaces},
  author = {Charles F. Doran and Alan Thompson},
  journal= {arXiv preprint arXiv:1709.00856},
  year   = {2018}
}

Comments

Final version; accepted for publication in "Communications in Number Theory and Physics"