On the blow-up formula of twisted de Rham cohomology

  • Youming ChenEmail author
  • Song Yang


We derive a blow-up formula for the de Rham cohomology of a local system of complex vector spaces on a compact complex manifold. As an application, we obtain the blow-up invariance of \(E_{1}\)-degeneracy of the Hodge–de Rham spectral sequence associated with a local system of complex vector spaces.


Local system Twisted de Rham cohomology Blow-up Hodge–de Rham spectral sequence 

Mathematics Subject Classification

32S45 14F40 32C35 



The authors would like to thank the Departments of Mathematics of Pennsylvania State University and Università degli Studi di Milano for the hospitalities during their respective visits, and thank Sheng Rao and Xiangdong Yang for the useful discussions. In particular, the authors would like to thank the referee for introducing Example 1 to them. This work is partially supported by the NSFC (Grant Nos. 11571242, 11701414), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJ1709216) and the China Scholarship Council.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of ScienceChongqing University of TechnologyChongqingPeople’s Republic of China
  2. 2.Center for Applied MathematicsTianjin UniversityTianjinPeople’s Republic of China

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