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

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.

arXiv comment23 pages; major changes in Section 5 concerning the dimension estimates of the kernel of homogeneous derivations