Complex immersions and Quillen metrics
type: Item
instance of: scholarly article
title: Complex immersions and Quillen metrics
zbMATH Open document ID: 0784.32010
DOI: 10.1007/BF02699352
author: Gilles Lebeau
author: Jean-Michel Bismut
published in: Publications Mathématiques
publication date: 1993-02-18T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/104077
review text: The authors' work is devoted to the proof of a certain (integral) formula which is an essential ingredient in the arithmetic Riemann-Roch of Gillet and Soulé. This integral formula is an expression for the logarithm of the norm (with respect to Quillen metrics) of a certain canonical section associated to determinant line bundles of a vector bundle on \(Y\) and a resolution of it with respect to a complex immersion \(Y\hookrightarrow X\). The integrals contain Todd classes and the additive genus \(R(x)\) of Gillet and Soulé. The paper is clearly written, very well organized and essentially self- contained. For this reason it is also accessable to non-experts.
reviewed by: Siegmund Kosarew
Mathematics Subject Classification ID: 32C35
Mathematics Subject Classification ID: 14C40
zbMATH DE Number: 123279
zbMATH Keywords: arithmetic Riemann-Roch
zbMATH Keywords: Quillen metrics
zbMATH Keywords: analytic torsion
MaRDI profile type: Publication
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OpenAlex ID: W1982733397
description: scientific article; zbMATH DE number 123279