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Stelzig, Jonas (2021): The Double Complex of a Blow-up. In: International Mathematics Research Notices, Vol. 2021, No. 14: pp. 10731-10744

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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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