A remark on the Chern class of a tensor product
type: Item
instance of: scholarly article
title: A remark on the Chern class of a tensor product
zbMATH Open document ID: 0863.14007
DOI: 10.1007/BF02567807
author: Paolo Aluffi
author: Carel Faber
published in: Manuscripta Mathematica
publication date: 1996-06-05T00:00:00Z
full work available at URL: https://eudml.org/doc/156112
review text: Let \(X\) be any algebraic scheme over a field, and let \(\alpha\in K^0(X)\). Then \(\alpha\) has a well-defined rank \(\text{rk} \alpha\), and Chern classes \(c_k(\alpha)\). We consider \(\alpha\otimes [{\mathcal L}]\), where \({\mathcal L}\) is an arbitrary line bundle on \(X\). Theorem. \(c_{\text{rk} \alpha+1} (\alpha)= c_{\text{rk} \alpha+1} (\alpha\otimes [{\mathcal L}])\).
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 14C35
zbMATH DE Number: 866152
zbMATH Keywords: Grothendieck group
zbMATH Keywords: tensor product of vector bundles
Wikidata QID: Q60145535
MaRDI profile type: Publication
cites work: Q3328651
OpenAlex ID: W1992525549
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description: scientific article; zbMATH DE number 866152