{"title":"任意场上slc曲面的丰度","authors":"Quentin Posva","doi":"10.46298/epiga.2023.volume7.8803","DOIUrl":null,"url":null,"abstract":"We prove the abundance conjecture for projective slc surfaces over arbitrary\nfields of positive characteristic. The proof relies on abundance for lc\nsurfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon\nand Xu to descend semi-ampleness from the normalization. We also present\napplications to dlt threefold pairs, and to mixed characteristic families of\nsurfaces.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Abundance for slc surfaces over arbitrary fields\",\"authors\":\"Quentin Posva\",\"doi\":\"10.46298/epiga.2023.volume7.8803\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove the abundance conjecture for projective slc surfaces over arbitrary\\nfields of positive characteristic. The proof relies on abundance for lc\\nsurfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon\\nand Xu to descend semi-ampleness from the normalization. We also present\\napplications to dlt threefold pairs, and to mixed characteristic families of\\nsurfaces.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-10-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/epiga.2023.volume7.8803\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2023.volume7.8803","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove the abundance conjecture for projective slc surfaces over arbitrary
fields of positive characteristic. The proof relies on abundance for lc
surfaces over abritrary fields, proved by Tanaka, and on the technique of Hacon
and Xu to descend semi-ampleness from the normalization. We also present
applications to dlt threefold pairs, and to mixed characteristic families of
surfaces.
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