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On the Group of Holomorphic Automorphisms of a Model Surface

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Abstract

In this paper, it is proved that the group \(\mathrm{Aut}\, Q\) of all holomorphic automorphisms of a holomorphically homogeneous nondegenerate model surface \(Q\) is a subgroup of the group of birational isomorphisms of the ambient complex space (the Cremona group) of uniformly bounded degree. The degree is estimated in terms of the dimension of the ambient space (Theorem 4). It is shown that no condition of the theorem can be weakened. In the paper, the question of the connectivity of \(\mathrm{Aut}\, Q\) is also considered (Theorem 7). This paper is directly adjacent to the previous paper of the author [7].

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, Moscow, Russia

    V. K. Beloshapka

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  1. V. K. Beloshapka
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Correspondence to V. K. Beloshapka.

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Beloshapka, V.K. On the Group of Holomorphic Automorphisms of a Model Surface. Russ. J. Math. Phys. 28, 275–283 (2021). https://doi.org/10.1134/S1061920821030018

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  • DOI: https://doi.org/10.1134/S1061920821030018

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