Morse–Novikov cohomology for blow-ups of complex manifolds

The weight $𝜃$ -sheaf ${\underline{ℝ}}_{X, 𝜃}$ 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.

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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

Vol. 320, No. 2, 2022

Lingxu Meng

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors