{"title":"通过基点无阈值实现高阶嵌入","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":"{\"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}","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}
引用次数: 0
摘要
在本论文中，我们将江（Jiang）和帕雷希（Pareschi）提出的极化无性无基点阈值与 k k -jet 非常振幅性联系起来。然后，我们推导出这一事实的若干应用，包括库默尔变项 k k -非常振幅的判据。
Higher order embeddings via the basepoint-freeness threshold
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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