The Double Complex of a Blow-up

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).

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