Morse-Novikov cohomology on complex manifolds
Differential Geometry
2020-02-04 v4 Complex Variables
Abstract
We view Dolbeault-Morse-Novikov cohomology H^{p,q}_\eta(X) as the cohomology of the sheaf \Omega_{X,\eta}^p of \eta-holomorphic p-forms and give several bimeromorphic invariants. Analogue to Dolbeault cohomology, we establish the Leray-Hirsch theorem and the blow-up formula for Dolbeault-Morse-Novikov cohomology. At last, we consider the relations between Morse-Novikov cohomology and Dolbeault-Morse-Novikov cohomology, moreover, investigate stabilities of their dimensions under the deformations of complex structures. In some aspects, Morse-Novikov and Dolbeault-Morse-Novikov cohomology behave similarly with de Rham and Dolbeault cohomology.
Keywords
Cite
@article{arxiv.1808.01057,
title = {Morse-Novikov cohomology on complex manifolds},
author = {Lingxu Meng},
journal= {arXiv preprint arXiv:1808.01057},
year = {2020}
}
Comments
16 page, Theorem 4.6 and 4.9 were added