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Unpublished Paper
Mirror Symmetry for Log Calabi-Yau Surfaces I
Mathematiques de l'IHES (2015)
  • Mark Gross
  • Paul Hacking, University of Massachusetts - Amherst
  • Sean Keel

We give a cononical sythetic 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 on the Gromov-Witten theory of the pair (Y,D)

Publication Date
March, 2015
Prepublished version downloaded from ArXiv. Published version is located at
Citation Information
Mark Gross, Paul Hacking and Sean Keel. "Mirror Symmetry for Log Calabi-Yau Surfaces I" Mathematiques de l'IHES (2015)
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