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Morse–Novikov cohomology for blow-ups of complex manifolds

Lingxu Meng

Vol. 320 (2022), No. 2, 365–390
Abstract

The weight 𝜃-sheaf ¯X,𝜃 helps us to reinterpret Morse–Novikov cohomologies via sheaf theory. We give several theorems of Künneth and Leray–Hirsch types. As applications, we prove that the 𝜃-Lefschetz number is independent of 𝜃 and calculate the Morse–Novikov cohomologies of projective bundles. Based on these results, we give two blow-up formulae on (not necessarily compact) complex manifolds, where the self-intersection formulae play a key role in establishing the explicit expressions for them.

Keywords
Morse–Novikov cohomology, blow-up, weight $\theta$-sheaf, self-intersection formula, Leray–Hirsch theorem
Mathematical Subject Classification
Primary: 53C56
Secondary: 55N35, 32Q55
Milestones
Received: 22 September 2021
Revised: 14 June 2022
Accepted: 13 September 2022
Published: 15 February 2023
Authors
Lingxu Meng
School of Mathematics
North University of China
Taiyuan
China