{"title":"Toric mirror monodromies and Lagrangian spheres","authors":"Vivek Shende","doi":"arxiv-2409.08261","DOIUrl":null,"url":null,"abstract":"The central fiber of a Gross-Siebert type toric degeneration is known to\nsatisfy homological mirror symmetry: its category of coherent sheaves is\nequivalent to the wrapped Fukaya category of a certain exact symplectic\nmanifold. Here we show that, in the Calabi-Yau case, the images of line bundles\nare represented by Lagrangian spheres.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Symplectic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08261","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The central fiber of a Gross-Siebert type toric degeneration is known to
satisfy homological mirror symmetry: its category of coherent sheaves is
equivalent to the wrapped Fukaya category of a certain exact symplectic
manifold. Here we show that, in the Calabi-Yau case, the images of line bundles
are represented by Lagrangian spheres.