A genericity theorem for algebraic stacks and essential dimension of hypersurfaces

Details A genericity theorem for algebraic stacks and essential dimension of hypersurfaces A genericity theorem for algebraic stacks and essential dimension of hypersurfaces

2011-03-08

arxiv.org/abs/1103.1611v2

Mathematics

Algebraic Geometry

25 pages. Several typos in version 1 have been corrected

Scientific paper

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.

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