The moduli space of maps from hypersurfaces and its Goodwillie tower

We define a moduli space of continuous maps from smooth hypersurfaces varying in an ample linear system. To study its topology, we construct a scanning map to an appropriate section space and investigate its effect on homology. Our main innovation is a general argument based on Goodwillie calculus and applicable to various moduli spaces of maps. Along the way, we compute the Goodwillie tower of the section space functor based at any retractive space.