Computations of Bott-Chern classes on P(E)

Christophe Mourougane (1)

1 IMJ - Institut de Mathématiques de Jussieu

We compute the Bott-Chern classes of the metric Eulersequence describing the relative tangent bundle of the variety P(E) of hyperplans of a holomorphic hermitian vector bundle (E,h) on a complex manifold.We give applications to the construction of the arithmetic characteristic classes of an arithmetic vector bundle and to the computation of the height of P(E)with respect to the tautological quotient bundle O_E(1).

Mots clés: Bott-Chern secondary classes; metric relative Euler sequence; arithmetic characteristic classes

Domaines: Géométrie algébrique [math.AG]

Christophe Mourougane. Computations of Bott-Chern classes on P(E). Duke Mathematical Journal, 2004, 124, pp.389-420. ⟨10.1215/S0012-7094-04-12425-X⟩. ⟨hal-00000364⟩