# Variation of the holomorphic determinant bundle

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.
Keywords :

Cited literature [35 references]

https://hal.archives-ouvertes.fr/hal-01301417
Contributor : Aigle I2m <>
Submitted on : Monday, November 18, 2019 - 10:59:07 PM
Last modification on : Thursday, January 23, 2020 - 6:22:16 PM

### File

Riemann-Roch-Deligne.pdf
Files produced by the author(s)

### Citation

Julien Grivaux. Variation of the holomorphic determinant bundle. Mathematical Research Letters, 2013, 20 (6), pp.1091--1101. ⟨10.4310/MRL.2013.v20.n6.a8⟩. ⟨hal-01301417⟩

Record views