Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case
Algebraic Geometry
2018-12-07 v2 Algebraic Topology
Complex Variables
Differential Geometry
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.
Keywords
Cite
@article{arxiv.1809.07277,
title = {Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case},
author = {Sheng Rao and Song Yang and Xiangdong Yang},
journal= {arXiv preprint arXiv:1809.07277},
year = {2018}
}
Comments
Final version with several typos fixed, to appear in Journal de Math\'ematiques Pures et Appliqu\'ees. 36 pages