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.
On the Szegö kernel of Cartan–Hartogs domains / Loi, Andrea; Uccheddu, Daria; Zedda, Michela. - In: ARKIV FÖR MATEMATIK. - ISSN 0004-2080. - 54:(2016), pp. 473-484. [10.1007/s11512-015-0228-9]
On the Szegö kernel of Cartan–Hartogs domains
ZEDDA, MICHELA
2016-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
