  The space of degree d smooth projective hypersurfaces of CP n admits a
scanning map to a certain space of sections. We compute a rational homotopy
model of the action by conjugation of the group U (n + 1) on this space of
sections, from which we deduce that the scanning map induces a monomorphism on
cohomology when d > 2. Our main technique is the rational homotopy theory of
Sullivan and, more specifically, a Sullivan model for the action by conjugation
of a connected topological group on a space of sections.
