The correspondence formula of Dolbeault complex on pair deformation

Jie Tu

The correspondence formula of Dolbeault complex on pair deformation

Differential Geometry 2019-05-21 v1 Complex Variables

Authors: Jie Tu

Abstract

Given a holomorphic family of pairs $\{(X_t,E_t)\}$ , where each $E_t$ is holomorphic vector bundle over compact complex manifold $X_t$ . For small enough $t$ , we get a correspondence between the Dolbeault complex of $E_t$ -valued $(p,q)$ -forms on $X_t$ and the one of $E_0$ -valued $(p,q)$ -forms on $X_0$ .

Keywords

holomorphic family of pairs dolbeault complex vector bundle compact complex manifold pair deformation

Cite

@article{arxiv.1905.08118,
  title  = {The correspondence formula of Dolbeault complex on pair deformation},
  author = {Jie Tu},
  journal= {arXiv preprint arXiv:1905.08118},
  year   = {2019}
}

Comments

12 pages

Related papers

View all related →