{"title":"Fibers over infinity of Landau–Ginzburg models","authors":"I. Cheltsov, V. Przyjalkowski","doi":"10.4310/cntp.2022.v16.n4.a1","DOIUrl":null,"url":null,"abstract":"We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety $X$ equals the dimension of the anticanonical system of $X$. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.","PeriodicalId":55616,"journal":{"name":"Communications in Number Theory and Physics","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2020-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Number Theory and Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cntp.2022.v16.n4.a1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety $X$ equals the dimension of the anticanonical system of $X$. We verify this conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.
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