On the blow-up formula of twisted de Rham cohomology

TL;DR

This paper establishes a blow-up formula for twisted de Rham cohomology on compact complex manifolds and demonstrates the invariance of spectral sequence degeneracy under blow-ups.

Contribution

It introduces a blow-up formula for de Rham cohomology with local systems and proves its invariance properties for spectral sequences.

Findings

Derived a blow-up formula for twisted de Rham cohomology.

Proved blow-up invariance of E1-degeneracy of the Hodge-de Rham spectral sequence.

Enhanced understanding of cohomological invariants under blow-up transformations.

Abstract

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 to a local system of complex vector spaces.