The fibred density property and the automorphism group of the spectral ball

TL;DR

This paper extends the density property concept to holomorphic fibrations, proves the spectral ball's fibration has this property, and characterizes its automorphism group, advancing understanding of complex geometric structures.

Contribution

It introduces the fibred density property, proves it for the spectral ball's natural fibration, and describes its automorphism group, providing new insights into complex manifolds.

Findings

Spectral ball's fibration has the fibred density property.

Automorphism group of the spectral ball is characterized.

Generalization of the density property to fibrations is established.

Abstract

We generalize the notion of the density property for complex manifolds to holomorphic fibrations, and introduce the notion of the fibred density property. We prove that the natural fibration of the spectral ball over the symmetrized polydisc enjoys the fibred density property and describe the automorphism group of the spectral ball.