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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.
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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⟩

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