The envelope of holomorphy of a model third-degree surface and the rigidity phenomenon |
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Authors: | R V Gammel I G Kossovskii |
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Institution: | (1) Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow, 119992, Russia |
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Abstract: | The structures of the graded Lie algebra aut Q infinitesimal automorphisms of a cubic (a model surface in ?N) and the corresponding group Aut Q of its holomorphic automorphisms are studied. It is proved that for any nondegenerate cubic, the positively graded components of the algebra aut Q are trivial and, as a consequence, Aut Q has no subgroups consisting of nonlinear automorphisms of the cubic that preserve the origin (the so-called rigidity phenomenon). In the course of the proof, the envelope of holomorphy for a nondegenerate cubic is constructed and shown to be a cylinder with respect to the cubic variable whose base is a Siegel domain of the second kind. |
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