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).
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