Hypercohomologies of truncated twisted holomorphic de Rham complexes

Abstract

We investigate the hypercohomologies of truncated twisted holomorphic de Rham complexes on (not necessarily compact) complex manifolds. In particular, we generalize Leray-Hirsch, Künneth and Poincaré-Serre duality theorems on them. At last, a blowup formula is given, which affirmatively answers a question posed by Chen, Y. and Yang, S. in [3].