2015/11/07 by Mark Gross, Paul Hacking, Sean Keel · 1 citation
paper · doi:10.1007/s10240-015-0073-1
crossref created 2015/03/24 · crossref issued 2015/11/07 · crossref published 2015/11/07 · crossref published-online 2015/11/07 · crossref deposited 2026/02/17 · crossref indexed 2026/08/02
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 on the Gromov-Witten theory of the pair ( Y , D ).