Abstract
The structures of the graded Lie algebra aut Q infinitesimal automorphisms of a cubic (a model surface in ℂN) 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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