Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case

Sheng Rao, Song Yang, Xiangdong Yang

Published 2018-09-19Version 1

We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples associated to the vanishing theorems of Girbau, Green-Lazarsfeld in a uniform manner and study the blow-up invariance of some classical holomorphic invariants.