Geodesic
A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 1999-2026

Voir la notice de l'article provenant de la source EMS Press

We compute the essential dimension of the functors Formsn,d​ and Hypersurfn,d​ of equivalence classes of homogeneous polynomials in n variables and hypersurfaces in Pn−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.
DOI : 10.4171/jems/411
Classification : 14-XX
Keywords: essential dimension, hypersurface, genericity theorem, stack, gerbe 
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Zinovy Reichstein; Angelo Vistoli. A genericity theorem for algebraic stacks and essential dimension of hypersurfaces. Journal of the European Mathematical Society, Tome 15 (2013) no. 6, pp. 1999-2026. doi: 10.4171/jems/411

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