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A matrix Poincaré formula for holomorphic automorphisms of quadrics of higher codimension. Real associative quadrics. (English) Zbl 0957.32016
The problem of the description of holomorphic automorphisms of quadrics dates back to the work of Poincaré. In this paper, the authors describe the holomorphic automorphisms of two infinite series of Hermitian quadrics. They give explicit formulas for the automorphisms in terms of rational maps. The quadrics in question are: quadric of real codimension two and a special class of quadric, the “real associated quadric”. The latest are quadrics that admit a ‘matrix Poincaré formula’ construction.

##### MSC:
 32V40 Real submanifolds in complex manifolds 32M05 Complex Lie groups, group actions on complex spaces