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Morse-Novikov Cohomology on Complex Manifolds

  • Lingxu MengEmail author
Article
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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

Morse–Novikov cohomology Weight \(\theta \)-sheaf Dolbeault–Morse–Novikov cohomology Leray–Hirsch theorem Blow-up formula Sheaf of \(\eta \)-holomorphic functions Bimeromorphic \(\theta \)-betti number \(\eta \)-hodge number Stability 

Mathematics Subject Classification

32C35 57R19 

Notes

Acknowledgements

I would like to express my gratitude to referees for their helpful suggestions and careful reading of my manuscript.

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Copyright information

© Mathematica Josephina, Inc. 2019

Authors and Affiliations

  1. 1.Department of MathematicsNorth University of ChinaTaiyuanPeople’s Republic of China

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