Vol. 14, No. 6, 2021

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A splitting lemma for coherent sheaves

Luca Studer

Vol. 14 (2021), No. 6, 1761–1772
Abstract

The presented splitting lemma extends the techniques of Gromov and Forstnerič to glue local sections of a given analytic sheaf, a key step in the proof of all Oka principles. The novelty on which the proof depends is a lifting lemma for transition maps of coherent sheaves, which yields a reduction of the proof to the work of Forstnerič. As applications we get shortcuts in the proofs of Forster and Ramspott’s Oka principle for admissible pairs and of the interpolation property of sections of elliptic submersions, an extension of Gromov’s results obtained by Forstnerič and Prezelj.

Keywords
Oka theory, Oka principle, splitting lemma
Mathematical Subject Classification 2010
Primary: 32L05
Milestones
Received: 31 January 2019
Revised: 29 October 2019
Accepted: 16 March 2020
Published: 7 September 2021
Authors
Luca Studer
Facultad de Ciencias Matemáticas
Universidad Complutense de Madrid
Madrid
Spain