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On the Szegö kernel of Cartan–Hartogs domains

Andrea Loi Dipartimento di Matematica e Informatica, Università di Cagliari Daria Uccheddu Dipartimento di Matematica e Informatica, Università di Cagliari Michela Zedda Dipartimento di Matematica “G. Peano”, Università di Torino

Differential Geometry mathscidoc:1701.10007

Arkiv for Matematik, 1-12, 2014.10
Inspired by the work of Z. Lu and G. Tian (Duke Math. J. 125:351–387,2004) in the compact setting, in this paper we address the problem of studying the Szegö kernel of the disk bundle over a noncompact Kähler manifold. In particular we compute the Szegö 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 ideas given in (Arezzo, Loi and Zuddas in Math. Z. 275:1207–1216,2013) for the computation of the Szegö kernel of the disk bundle over an Hermitian symmetric space of compact type.
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@inproceedings{andrea2014on,
  title={On the Szegö kernel of Cartan–Hartogs domains},
  author={Andrea Loi, Daria Uccheddu, and Michela Zedda},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406870274817},
  booktitle={Arkiv for Matematik},
  pages={1-12},
  year={2014},
}
Andrea Loi, Daria Uccheddu, and Michela Zedda. On the Szegö kernel of Cartan–Hartogs domains. 2014. In Arkiv for Matematik. pp.1-12. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406870274817.
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