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arXiv · 1410.1508

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

Andrea Loi·Daria Uccheddu·Michela Zedda
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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.

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Andrea Loi, Daria Uccheddu, Michela Zedda. 2014-10-06. On the Szeg\"o kernel of Cartan-Hartogs domains. https://doi.org/10.1007/s11512-015-0228-9

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