{"title":"On the complex affine structures of SYZ-fibration of del Pezzo surfaces","authors":"Siu-Cheong Lau, Tsung-Ju Lee, Yu-Shen Lin","doi":"10.4310/atmp.2022.v26.n6.a7","DOIUrl":null,"url":null,"abstract":"Given any smooth cubic curve $E \\subseteq \\mathbb{P}^2$, we show that the complex affine structure of the special Lagrangian fibration of $\\mathbb{P}^2 \\: \\backslash \\: E$ constructed by Collins–Jacob–Lin [<b>12</b>] coincides with the affine structure used in Carl–Pomperla–Siebert [<b>15</b>] 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.","PeriodicalId":50848,"journal":{"name":"Advances in Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.4310/atmp.2022.v26.n6.a7","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Given any smooth cubic curve $E \subseteq \mathbb{P}^2$, we show that the complex affine structure of the special Lagrangian fibration of $\mathbb{P}^2 \: \backslash \: E$ 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.
期刊介绍:
Advances in Theoretical and Mathematical Physics is a bimonthly publication of the International Press, publishing papers on all areas in which theoretical physics and mathematics interact with each other.