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Abstract
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The weight
-sheaf
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
-Lefschetz number
is independent of
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
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Mathematical Subject Classification
Primary: 53C56
Secondary: 55N35, 32Q55
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Milestones
Received: 22 September 2021
Revised: 14 June 2022
Accepted: 13 September 2022
Published: 15 February 2023
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