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arXiv · 1106.4977

Mirror symmetry for log Calabi-Yau surfaces I

Mark Gross·Paul Hacking·Sean Keel
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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.

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Mark Gross, Paul Hacking, Sean Keel. 2011-06-24. Mirror symmetry for log Calabi-Yau surfaces I. https://arxiv.org/abs/1106.4977

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