On the complex affine structures of SYZ fibration of Del Pezzo surfaces
Files
First author draft
Date
2020
DOI
Authors
Lau, Siu
Lee, Tsung-Ju
Lin, Yu-Shen
Version
First author draft
OA Version
Citation
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.
Abstract
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 [12]
coincides with the affine structure used in Carl-Pomperla-Siebert [15] 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.