Mirror symmetry for log Calabi-Yau surfaces I
Abstract
We give a canonical synthetic construction of the mirror family to a pair (Y,D) of a smooth projective surface with an anti-canonical cycle of rational curves, as the spectrum of an explicit algebra defined in terms of counts of rational curves on Y meeting D in a single point. In the case D is contractible, the family gives a smoothing of the dual cusp, and thus a proof of Looijenga's 1981 cusp conjecture.
Keywords
Cite
@article{arxiv.1106.4977,
title = {Mirror symmetry for log Calabi-Yau surfaces I},
author = {Mark Gross and Paul Hacking and Sean Keel},
journal= {arXiv preprint arXiv:1106.4977},
year = {2015}
}
Comments
144 pages, 3 figures, Second version significantly shorter, 109 pages. The first version has a lot of material (particularly in the introduction and material on cyclic quotient singularities) which does not appear in the new version. Download version 1 if this material is desired. Third and final version, small changes from Version 2, to appear in Publ. IHES