A note on birational transformations belonging to Galois points

摘要

Let P ε{lunate} P~(n+1) be a Galois point for a hypersurface X ? P~(n+1). Then every element of the Galois group G_P induces a birational transformation of X. In this note, we study this birational transformation. In particular, for smooth cubic hypersurface, we determine the condition when the birational transformation becomes a linear one.