Complex manifolds admitting proper actions of high-dimensional groups

Alexander Isaev*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    We explicitly classify all pairs (M, G), where M is a connected complex manifold of dimension n ≥ 2 and G is a connected Lie group acting properly and effectively on M by holomorphic transformations and having dimension d G satisfying n2 + 2 ≤ dG < n2 + 2n. We also consider the case dG = n2 + 1. In this case all actions split into three types according to the form of the linear isotropy subgroup. We give a complete explicit description of all pairs (M, G) for two of these types, as well as a large number of examples of actions of the third type. These results complement a theorem due to W. Kaup for the maximal group dimension n2 + 2n and generalize some of the author's earlier work on Kobayashi-hyperbolic manifolds with high-dimensional holomorphic automorphism group.

    Original languageEnglish
    Pages (from-to)141-160
    Number of pages20
    JournalJournal of Lie Theory
    Issue number1
    Publication statusPublished - 2008


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