English

On the Szeg\"o kernel of Cartan-Hartogs domains

Differential Geometry 2016-10-12 v1 Complex Variables

Abstract

Inspired by the work of Z. Lu and G. Tian [21] in the compact setting, in this paper we address the problem of studying the Szeg\"o kernel of the disk bundle over a noncompact K\"ahler manifold. In particular we compute the Szeg\"o kernel of the disk bundle over a Cartan-Hartogs domain based on a bounded symmetric domain. The main ingredients in our analysis are the fact that every Cartan-Hartogs domain can be viewed as an "iterated" disk bundle over its base and the the ideas given in [4] for the computation of the Szeg\"o kernel of the disk bundle over an Herimitian symmetric space of compact type.

Keywords

Cite

@article{arxiv.1410.1508,
  title  = {On the Szeg\"o kernel of Cartan-Hartogs domains},
  author = {Andrea Loi and Daria Uccheddu and Michela Zedda},
  journal= {arXiv preprint arXiv:1410.1508},
  year   = {2016}
}

Comments

11 pp