{"title":"ON THE ANTI-CANONICAL GEOMETRY OF WEAK -FANO THREEFOLDS, III","authors":"Chen Jiang, Yu-Xi Zou","doi":"10.1017/nmj.2023.17","DOIUrl":null,"url":null,"abstract":"\n\t <jats:p>For a terminal weak <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002776302300017X_inline2.png\" />\n\t\t<jats:tex-math>\n${\\mathbb {Q}}$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula>-Fano threefold <jats:italic>X</jats:italic>, we show that the <jats:italic>m</jats:italic>th anti-canonical map defined by <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002776302300017X_inline3.png\" />\n\t\t<jats:tex-math>\n$|-mK_X|$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula> is birational for all <jats:inline-formula>\n\t <jats:alternatives>\n\t\t<jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S002776302300017X_inline4.png\" />\n\t\t<jats:tex-math>\n$m\\geq 59$\n</jats:tex-math>\n\t </jats:alternatives>\n\t </jats:inline-formula>.</jats:p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/nmj.2023.17","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
For a terminal weak
${\mathbb {Q}}$
-Fano threefold X, we show that the mth anti-canonical map defined by
$|-mK_X|$
is birational for all
$m\geq 59$
.
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