Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case
arXiv:1809.07277
Abstract
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, Kawamata-Viehweg and Green-Lazarsfeld in a uniform manner and study the blow-up invariance of some classical holomorphic invariants.
Final version with several typos fixed, to appear in Journal de Mathématiques Pures et Appliquées. 36 pages