On the complex affine structures of SYZ fibration of Del Pezzo surfaces
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Citation (published version)Siu Lau, Tsung-Ju Lee, Yu-Shen Lin. "On the Complex Affine Structures of SYZ Fibration of Del Pezzo Surfaces." https://arxiv.org/abs/2005.04825.
Given any smooth cubic curve E ⊆ P^2, we show that the complex affine structure of the special Lagrangian fibration of P^2 ⧵ E constructed by Collins-Jacob-Lin  coincides with the affine structure used in Carl-Pomperla-Siebert  for constructing mirror. Moreover, we use the Floer-theoretical gluing method to construct a mirror using immersed Lagrangians, which is shown to agree with the mirror constructed by Carl-Pomperla-Siebert.