{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/proc/16901","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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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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