The mirror of the cubic surface
Algebraic Geometry
2019-10-21 v1 Symplectic Geometry
Abstract
This paper expands on a remark in the paper "Mirror Symmetry for Log Calabi-Yau Surfaces I" of the first three authors of this paper, explaining fully how various constructions of the authors apply to give the mirror to the cubic surface. We give a full description of the scattering diagram associated to the cubic surface: this is a particularly nice diagram in which rays of every rational slope occur, but they may all be described. The equation of the mirror cubic family is then derived in two ways, first by using broken lines and then by using more recent constructions involving a direct calculation of Gromov-Witten invariants.
Cite
@article{arxiv.1910.08427,
title = {The mirror of the cubic surface},
author = {Mark Gross and Paul Hacking and Sean Keel and Bernd Siebert},
journal= {arXiv preprint arXiv:1910.08427},
year = {2019}
}
Comments
30 pages, accepted version for Miles Reid's 70th birthday proceedings