Direct Images and Hilbert Fields

TL;DR

This paper investigates the curvature operator of Bergman space fields linked to holomorphic fibrations of Kähler manifolds, especially for smoothly bounded pseudoconvex domains, providing insights into their geometric properties.

Contribution

It offers a detailed analysis of the curvature operator in the context of Bergman spaces over pseudoconvex domains within Kähler fibrations, advancing understanding of their geometric structure.

Findings

Curvature operator characterized for Bergman space fields

Results applicable to pseudoconvex domains in Kähler fibrations

Enhanced understanding of geometric properties of these fields

Abstract

In this article we undertake a careful study of the curvature operator of a field of Bergman spaces associated to a holomorphic fibration of K\"ahler manifolds. We focus on the case when the fibers are smoothly bounded pseudoconvex domains.