On the blow-up formula of twisted de Rham cohomology

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 with a local system of complex vector spaces.

Hypercohomologies of truncated twisted holomorphic de Rham complexes

“…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].…”

“…Recently, the blowup formula on the de Rham cohomology with values in a local system were studied with different approaches [3,7,14,5]. More generally, Chen, Y. and Yang, S. posed a question on the existence of the blowup formula on the hypercohomology of a truncated twisted holomorphic de Rham complex ([3, Question 10]).…”

Mayer-Vietoris systems and their applications

“…As applications of this theorem, we generalize the main results in [6,20,21]. During our preparation of the present work, Rao, S., Yang, S. and Yang, X.-D. ( [21]) gave a blow-up formula for bundle-valued Dolbeault cohomology on compact complex manifolds.…”

“…During our preparation of the present work, Rao, S., Yang, S. and Yang, X.-D. ( [21]) gave a blow-up formula for bundle-valued Dolbeault cohomology on compact complex manifolds. With the similar way in [21], Chen, Y. and Yang, S. ( [6]) gave a blow-up formula for cohomology with values in local systems on compact complex manifolds. By Theorem 1.1, we will give other formulas in a different way and remove the compactness.…”

Blow-up formulae for twisted cohomologies with supports

“…Recently, there are some progress on the complex blow-up formulae for twisted cohomologies. On compact complex manifolds, complex blow-up formulae were established for twisted Dolbeault cohomologies [28,29,1,31,32] and twisted de Rham cohomologies [37,36,8,40]. In different approaches, we [20,21,22,23] established and explicitly expressed these formulae on arbitrary complex manifolds without the hypothesis of compactness.…”