Mirror symmetry for log Calabi-Yau surfaces I

@article{Gross2011MirrorSF,
  title={Mirror symmetry for log Calabi-Yau surfaces I},
  author={M. Gross and Paul Hacking and S. Keel},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2011},
  volume={122},
  pages={65-168}
}
  • M. Gross, Paul Hacking, S. Keel
  • Published 2011
  • Mathematics
  • Publications mathématiques de l'IHÉS
  • We give a canonical synthetic construction of the mirror family to pairs (Y,D) where Y is a smooth projective surface and D is an anti-canonical cycle of rational curves. This mirror family is constructed as the spectrum of an explicit algebra structure on a vector space with canonical basis and multiplication rule defined in terms of counts of rational curves on Y meeting D in a single point. The elements of the canonical basis are called theta functions. Their construction depends crucially… CONTINUE READING
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