Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry
arXiv:1605.00342
Abstract
We carry out the SYZ program for the local Calabi--Yau manifolds of type by developing an equivariant SYZ theory for the toric Calabi--Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov--Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood--Iqbal--Vafa.
arXiv commentv3: 43 pages, 12 figures, improved exposition
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- Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
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