{"title":"某些环状法诺超曲面的公因子 SYZ 猜想","authors":"Yang Li","doi":"10.4310/cjm.2024.v12.n1.a3","DOIUrl":null,"url":null,"abstract":"We prove the metric version of the SYZ conjecture for a class of Calabi–Yau hypersurfaces inside toric Fano manifolds, by solving a variational problem whose minimizer may be interpreted as a global solution of the real Monge–Ampère equation on certain polytopes. This does not rely on discrete symmetry.","PeriodicalId":48573,"journal":{"name":"Cambridge Journal of Mathematics","volume":"87 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Metric SYZ conjecture for certain toric Fano hypersurfaces\",\"authors\":\"Yang Li\",\"doi\":\"10.4310/cjm.2024.v12.n1.a3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the metric version of the SYZ conjecture for a class of Calabi–Yau hypersurfaces inside toric Fano manifolds, by solving a variational problem whose minimizer may be interpreted as a global solution of the real Monge–Ampère equation on certain polytopes. This does not rely on discrete symmetry.\",\"PeriodicalId\":48573,\"journal\":{\"name\":\"Cambridge Journal of Mathematics\",\"volume\":\"87 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-01-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Cambridge Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/cjm.2024.v12.n1.a3\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Cambridge Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cjm.2024.v12.n1.a3","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Metric SYZ conjecture for certain toric Fano hypersurfaces
We prove the metric version of the SYZ conjecture for a class of Calabi–Yau hypersurfaces inside toric Fano manifolds, by solving a variational problem whose minimizer may be interpreted as a global solution of the real Monge–Ampère equation on certain polytopes. This does not rely on discrete symmetry.
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