Computations of Bott-Chern classes on \(\mathbb{P}(E)\). (English) Zbl 1064.14022

Mourougane, Christophe

Duke Math. J. 124, No. 2, 389-420 (2004).

Bott-Chern classes of the metrized relative Euler sequence describing the relative tangent bundle of the variety \(\mathbb P(E)\) of hyperplanes in a holomorphic Hermitian vector bundle \((E,h)\) on a complex manifold are computed. Applications to the construction of the arithmetic characteristic classes of an arithmetic vector bundle \({\overline{E}}\) and to the computation of the height of \(\mathbb P({\overline{E}})\) with respect to the tautological quotient bundle \({\mathcal O}_{\overline{E}}(1)\) are also presented.

Reviewer: Gheorghe Pitiş (Braşov)

MSC:

14G40	Arithmetic varieties and schemes; Arakelov theory; heights
53C55	Global differential geometry of Hermitian and Kählerian manifolds
32L05	Holomorphic bundles and generalizations

Keywords:

holomorphic vector bundle; Euler sequence

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