On special quadratic birational transformations of a projective space   into a hypersurface
  We study transformations as in the title with emphasis on those having smooth connected base locus, called "special". In particular, we classify all special quadratic birational maps into a quadric hypersurface whose inverse is given by quadratic forms by showing that there are only four examples having general hyperplane sections of Severi varieties as base loci. 
Giovanni Staglian\`o
math.AG