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.
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Acknowledgements
The authors would like to thank the referee for recommendations to improve the presentation and for pointing out some problems in the first version of this article. Moreover they would like to thank A. Liendo, P.-M. Poloni, S. Maubach, A. van den Essen, H. Derksen and A. Nowicki for discussions about determining the dimension growth of the kernel of a homogeneous derivation and finally again the referee for the contribution of the Proposition 5.2 and its proof which simplified the calculations.
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Andrist, R.B., Kutzschebauch, F. The fibred density property and the automorphism group of the spectral ball. Math. Ann. 370, 917–936 (2018). https://doi.org/10.1007/s00208-017-1520-8
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DOI: https://doi.org/10.1007/s00208-017-1520-8