Chern classes of vector bundles on arithmetic varieties

Tohru Nakashima, Yuichiro Takeda

Research output: Contribution to journalArticle

Abstract

Let F̄ be a Hermitian vector bundle on an arithmetic variety X over ℤ. We prove an inequality between the L2-norm of an element in H1(X,FV) and arithmetic Chern classes of F under certain stability condition. This is a higher dimensional analogue of a result of C. Soulé for Hermitian line bundles on arithmetic surfaces. We observe that our result is related to a conjectural inequality of Miyaoka-Yau type.

Original languageEnglish
Pages (from-to)205-216
Number of pages12
JournalPacific Journal of Mathematics
Volume176
Issue number1
DOIs
Publication statusPublished - Jan 1 1996
Externally publishedYes

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Chern Classes
Vector Bundle
Line Bundle
Stability Condition
High-dimensional
Analogue
Norm

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Chern classes of vector bundles on arithmetic varieties. / Nakashima, Tohru; Takeda, Yuichiro.

In: Pacific Journal of Mathematics, Vol. 176, No. 1, 01.01.1996, p. 205-216.

Research output: Contribution to journalArticle

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