Morse-Novikov cohomology on complex manifolds

Abstract

We view Dolbeault-Morse-Novikov cohomology H^{p,q}_η(X) as the cohomology of the sheaf Ω_{X,η}^p of η-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.

arXiv comment16 page, Theorem 4.6 and 4.9 were added

References in corpus (5)

• Morse-Novikov cohomology of locally conformally Kähler manifolds
• Moser stability for locally conformally symplectic structures
• Morse-Novikov cohomology on complex manifolds
• Morse-Novikov cohomology for blow-ups of complex manifolds
• Weighted Bott-Chern and Dolbeault cohomology for LCK-manifolds with potential

Cited by in corpus (6)

• Morse-Novikov cohomology on complex manifolds
• Mayer-Vietoris systems and their applications
• Hypercohomologies of truncated twisted holomorphic de Rham complexes
• Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology
• Blow-up formulae for twisted cohomologies with supports
• Holomorphic Euler number of K$\ddot{a}$hler manifolds with almost nonnegative Ricci curvature