On the complex affine structures of SYZ fibration of del Pezzo surfaces

Siu Cheong Lau; Tsung Ju Lee; Yu Shen Lin

doi:10.4310/ATMP.2022.v26.n6.a7

On the complex affine structures of SYZ fibration of del Pezzo surfaces

Siu Cheong Lau, Tsung Ju Lee, Yu Shen Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Given any smooth cubic curve E ⊆ ℙ², we show that the complex affine structure of the special Lagrangian fibration of ℙ² \ 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.

Original language	English
Pages (from-to)	1837-1872
Number of pages	36
Journal	Advances in Theoretical and Mathematical Physics
Volume	26
Issue number	6
DOIs	https://doi.org/10.4310/ATMP.2022.v26.n6.a7
Publication status	Published - 2023

All Science Journal Classification (ASJC) codes

General Mathematics
General Physics and Astronomy

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10.4310/ATMP.2022.v26.n6.a7

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abstract = "Given any smooth cubic curve E ⊆ ℙ2, we show that the complex affine structure of the special Lagrangian fibration of ℙ2 \ 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.",

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year = "2023",

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AU - Lee, Tsung Ju

AU - Lin, Yu Shen

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N2 - Given any smooth cubic curve E ⊆ ℙ2, we show that the complex affine structure of the special Lagrangian fibration of ℙ2 \ 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.

AB - Given any smooth cubic curve E ⊆ ℙ2, we show that the complex affine structure of the special Lagrangian fibration of ℙ2 \ 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.

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JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

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On the complex affine structures of SYZ fibration of del Pezzo surfaces

Abstract

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