On the Morse–Novikov Cohomology of blowing up complex manifolds

Abstract

Inspired by the recent works of S. Rao-S. Yang-X.-D. Yang and L. Meng on the blow-up formulae for de Rham and Morse-Novikov cohomology groups, we give a new simple proof of the blow-up formula for Morse-Novikov cohomology by introducing the relative Morse-Novikov cohomology group via sheaf cohomology theory and presenting the explicit isomorphism therein.

Blow-up formulae for twisted cohomologies with supports

“…Recently, there are some progress on the complex blow-up formulae for twisted cohomologies. On compact complex manifolds, complex blow-up formulae were established for twisted Dolbeault cohomologies [28,29,1,31,32] and twisted de Rham cohomologies [37,36,8,40]. In different approaches, we [20,21,22,23] established and explicitly expressed these formulae on arbitrary complex manifolds without the hypothesis of compactness.…”

Bott-Chern hypercohomology and bimeromorphic invariants

“…Recently, extensive works have been done on the topics of blow-up formulae and the ∂ ∂-lemma. We refer the readers to [6], [7], [14], [42], [28], [29], [30], [31], [32], [51], [53], [47], [23], [22], [34], [38] etc., and the references therein for some resent results.…”