Abstract
Let V be a smooth hypersurface in P n+1 . We consider a projection of V from P∈ P n+1 to a hyperplane H. This projection induces an extension of fields k( V)/ k( H), which does not depend on the choice of H. We study the structures of this extension and the hypersurfaces together. The point P is called a Galois point if the extension is Galois. We show estimates of the number of the Galois points and some rules of their distributions. Especially we give the defining equation of V with maximal number of Galois points.
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