  We compute the essential dimension of the functors Forms_{n,d} and
Hypersurf_{n, d} of equivalence classes of homogeneous polynomials in n
variables and hypersurfaces in P^{n-1}, respectively, over any base field k of
characteristic 0. Here two polynomials (or hypersurfaces) over K are considered
equivalent if they are related by a linear change of coordinates with
coefficients in K. Our proof is based on a new Genericity Theorem for algebraic
stacks, which is of independent interest. As another application of the
Genericity Theorem, we prove a new result on the essential dimension of the
stack of (not necessarily smooth) local complete intersection curves.
