Kodaira维数为零的三重积分Hodge猜想的失败

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2018-02-06 DOI:10.4171/cmh/479

Olivier Benoist, J. C. Ottem

{"title":"Kodaira维数为零的三重积分Hodge猜想的失败","authors":"Olivier Benoist, J. C. Ottem","doi":"10.4171/cmh/479","DOIUrl":null,"url":null,"abstract":"We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.","PeriodicalId":50664,"journal":{"name":"Commentarii Mathematici Helvetici","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2018-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.4171/cmh/479","citationCount":"21","resultStr":"{\"title\":\"Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero\",\"authors\":\"Olivier Benoist, J. C. Ottem\",\"doi\":\"10.4171/cmh/479\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.\",\"PeriodicalId\":50664,\"journal\":{\"name\":\"Commentarii Mathematici Helvetici\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2018-02-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.4171/cmh/479\",\"citationCount\":\"21\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Commentarii Mathematici Helvetici\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/cmh/479\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Commentarii Mathematici Helvetici","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/cmh/479","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 21

摘要

我们证明了Enriques曲面和亏格至少为1的非常一般的曲线的乘积不满足1-环的积分Hodge猜想。这提供了积分Hodge猜想失败的Kodaira维数为零的光滑投影复三重的第一个例子，以及光滑投影复三重上4次非代数扭转上同调类的第一个实例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Failure of the integral Hodge conjecture for threefolds of Kodaira dimension zero

We prove that the product of an Enriques surface and a very general curve of genus at least 1 does not satisfy the integral Hodge conjecture for 1-cycles. This provides the first examples of smooth projective complex threefolds of Kodaira dimension zero for which the integral Hodge conjecture fails, and the first examples of non-algebraic torsion cohomology classes of degree 4 on smooth projective complex threefolds.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.