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arXiv · 1605.00342

Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry

Atsushi Kanazawa·Siu-Cheong Lau
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Abstract

We carry out the SYZ program for the local Calabi--Yau manifolds of type $\widetilde{A}$ 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.

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Atsushi Kanazawa, Siu-Cheong Lau. 2016-05-02. Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry. https://arxiv.org/abs/1605.00342

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