2000 character limit reached
Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry (1605.00342v3)
Published 2 May 2016 in math.AG, hep-th, and math.SG
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.