TL;DR
This paper computes the double complex of differential forms on blow-ups and projective bundles over compact complex manifolds, providing formulas for various cohomologies such as de-Rham, Dolbeault, Bott-Chern, and Aeppli.
Contribution
It offers explicit formulas for the double complex and associated cohomologies of blow-ups and projective bundles, advancing understanding of their complex geometric structures.
Findings
Computed the double complex up to quasi-isomorphism.
Derived formulas for multiple cohomology theories.
Unified treatment of cohomologies for blow-ups and projective bundles.
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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