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A genericity theorem for algebraic stacks and essential dimension of hypersurfaces

Zinovy Reichstein, Angelo Vistoli (2013)

Journal of the European Mathematical Society

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 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...

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