Abstract
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 \mathbb 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.
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