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The Double Complex of a Blow-up

2018/08/31 by Jonas Stelzig
Mathematics · #Algebraic Geometry and Number Theory #Differential (mechanical device) #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematical analysis #Mathematics #Pure mathematics #math.AG #math.CV #math.DG #msc:32C35 #msc:32Q99

paper · pdf · doi:10.1093/imrn/rnz139

Inlcuded an example and discussions of product structures and extensions to singular spaces. Minor improvements throughout. Mainly following referee suggestions

arxiv created 2019/06/03 · openalex publication_date 2019/06/04 · arxiv updated 2019/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract We compute the double complex of smooth complex-valued differential forms on projective bundles over and blow-ups of compact complex manifolds up to a suitable notion of quasi-isomorphism. This simultaneously yields formulas for “all” cohomologies naturally associated with this complex (in particular, de Rham, Dolbeault, Bott–Chern, and Aeppli).

Citations