平面向量束的代数Chern类

IF 0.5 4区数学 Q3 MATHEMATICS

Manuscripta Mathematica Pub Date : 2023-11-09 DOI:10.1007/s00229-023-01518-y

Adrian Langer

{"title":"平面向量束的代数Chern类","authors":"Adrian Langer","doi":"10.1007/s00229-023-01518-y","DOIUrl":null,"url":null,"abstract":"Abstract We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch’s conjecture on Chern classes of flat vector bundles on smooth complex projective varieties but in some cases they give a more precise information. We also study Higgs version of Bloch’s conjecture and analogous problems in the positive characteristic case.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":" 90","pages":"0"},"PeriodicalIF":0.5000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On algebraic Chern classes of flat vector bundles\",\"authors\":\"Adrian Langer\",\"doi\":\"10.1007/s00229-023-01518-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch’s conjecture on Chern classes of flat vector bundles on smooth complex projective varieties but in some cases they give a more precise information. We also study Higgs version of Bloch’s conjecture and analogous problems in the positive characteristic case.\",\"PeriodicalId\":49887,\"journal\":{\"name\":\"Manuscripta Mathematica\",\"volume\":\" 90\",\"pages\":\"0\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Manuscripta Mathematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00229-023-01518-y\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Manuscripta Mathematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00229-023-01518-y","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

摘要在单群的某些假设下，证明了平面向量束的高Chern类的某些组合在Chow群中是挠性的。类似的结果也适用于变形为这种平面向量束的平面向量束(也适用于拟射影变体)。这些结果是由布洛赫关于光滑复射影变体上的平坦向量束的陈类的猜想所激发的，但在某些情况下它们给出了更精确的信息。我们还研究了希格斯版布洛赫猜想和正特征情况下的类似问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On algebraic Chern classes of flat vector bundles

查看原文本刊更多论文

On algebraic Chern classes of flat vector bundles

Abstract We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch’s conjecture on Chern classes of flat vector bundles on smooth complex projective varieties but in some cases they give a more precise information. We also study Higgs version of Bloch’s conjecture and analogous problems in the positive characteristic case.

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

Manuscripta Mathematica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.