Hypercohomologies of truncated twisted holomorphic de Rham complexes

TL;DR

This paper studies the hypercohomologies of truncated twisted holomorphic de Rham complexes on complex manifolds, generalizing classical theorems and providing a blowup formula that addresses a specific open question.

Contribution

It extends classical cohomological theorems to a broader setting and introduces a blowup formula for these complexes, answering an open question.

Findings

Generalized Leray-Hirsch, Künneth, and Poincaré-Serre duality theorems.

Established a blowup formula for hypercohomologies.

Addressed an open problem posed by Chen and Yang.

Abstract

We investigate the hypercohomologies of truncated twisted holomorphic de Rham complexes on (not necessarily compact) complex manifolds. In particular, we generalize Leray-Hirsch, K\"{u}nneth and Poincar\'{e}-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 \cite{CY}.