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arXiv · 1806.06622

Morse-Novikov cohomology for blow-ups of complex manifolds

Lingxu Meng
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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 K\"{u}nneth 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.

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Lingxu Meng. 2018-06-18. Morse-Novikov cohomology for blow-ups of complex manifolds. https://doi.org/10.2140/pjm.2022.320.365

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