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15 February 2025
 
  » arxiv » 1605.0342

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Local Calabi-Yau manifolds of affine type A and open Yau-Zaslow formula via SYZ mirror symmetry
Atsushi Kanazawa ; Siu-Cheong Lau ;
Date 2 May 2016
AbstractWe construct SYZ mirrors of the local Calabi-Yau manifolds of affine type A by developing an equivariant SYZ theory for the toric Calabi-Yau manifolds of infinite-type. The equations for the SYZ mirrors involve the Riemann theta functions and generating functions of the open Gromov-Witten invariants. We obtain explicit formulae for the generating functions which are open analogs of the Yau-Zaslow formula in dimension 2, and show that they have nice modular properties. We also relate the SYZ pairs with mirror symmetry for the abelian varieties and hypersurfaces therein.
Source arXiv, 1605.0342
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