Mathematical Research Letters
Volume 20 (2013)
Variation of the holomorphic determinant bundle
Pages: 1091 – 1101
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.