Abstract
We call a flag variety admissible if its automorphism group is the projective general linear group. (This holds in most cases.)
Let K be a field of characteristic 0, containing all roots of unity. Let the K-variety X be a form of an admissible flag variety. We prove that X is either ruled, or the automorphism group of X is bounded, meaning that there exists a constant C ∈ ℕ such that if G is a finite subgroup of AutK(X), then the cardinality of G is smaller than C.
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The research was partly supported by the National Research, Development and Innovation Office (NKFIH) Grant No. K120697. The project leading to this application has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 741420).
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GULD, A. BOUNDEDNESS PROPERTIES OF AUTOMORPHISM GROUPS OF FORMS OF FLAG VARIETIES. Transformation Groups 25, 1161–1184 (2020). https://doi.org/10.1007/s00031-020-09569-1
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DOI: https://doi.org/10.1007/s00031-020-09569-1