Mirror symmetry for log Calabi-Yau surfaces I

Details Mirror symmetry for log Calabi-Yau surfaces I Mirror symmetry for log Calabi-Yau surfaces I

2011-06-24

arxiv.org/abs/1106.4977v1

Mathematics

Algebraic Geometry

144 pages, 3 figures

Scientific paper

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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