{"title":"Higher order embeddings via the basepoint-freeness threshold","authors":"Federico Caucci","doi":"10.1090/proc/16901","DOIUrl":null,"url":null,"abstract":"<p>In this note, we relate the basepoint-freeness threshold of a polarized abelian variety, introduced by Jiang and Pareschi, with <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-jet very ampleness. Then, we derive several applications of this fact, including a criterion for the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k\"> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=\"application/x-tex\">k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-very ampleness of Kummer varieties.</p>","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"39 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the American Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/proc/16901","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this note, we relate the basepoint-freeness threshold of a polarized abelian variety, introduced by Jiang and Pareschi, with kk-jet very ampleness. Then, we derive several applications of this fact, including a criterion for the kk-very ampleness of Kummer varieties.
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