Mathematical Research Letters

Volume 20 (2013)

Number 6

Variation of the holomorphic determinant bundle

Pages: 1091 – 1101

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n6.a8

Author

Julien Grivaux (Centre national de la recherche scientifique, Université d’Aix-Marseille, France)

Abstract

In this paper, we prove that the Grothendieck-Riemann-Roch formula in Deligne cohomology computing the determinant of the cohomology of a holomorphic vector bundle on the fibers of a proper submersion between abstract complex manifolds is invariant by deformation of the bundle.

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