Morse-Novikov cohomology for blow-ups of complex manifolds

Abstract

The weight $\theta$-sheaf ${\underline{\mathbb{R}}}_{X,\theta }$ 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 $\theta$-Lefschetz number is independent of $\theta$ and calculate the Morse-Novikov cohomologies of projective bundles. Based on these results, we give two blow-up formulae on (\emph{not necessarily compact}) complex manifolds, where the self-intersection formulae play a key role in establishing the explicit expressions for them.

22 pages

References in corpus (5)

• Morse-Novikov cohomology of locally conformally Kähler manifolds
• Moser stability for locally conformally symplectic structures
• Mayer-Vietoris systems and their applications
• Morse-Novikov cohomology for blow-ups of complex manifolds
• Blow-up formulae for twisted cohomologies with supports

Cited by in corpus (3)

• The Double Complex of a Blow-up
• Morse-Novikov cohomology on complex manifolds
• Morse-Novikov cohomology for blow-ups of complex manifolds