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 
@article{JEMS_2013_15_6_a0,
     author = {Zinovy Reichstein and Angelo Vistoli},
     title = {A genericity theorem for algebraic stacks and essential dimension of hypersurfaces},
     journal = {Journal of the European Mathematical Society},
     pages = {1999--2026},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {2013},
     doi = {10.4171/jems/411},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/411/}
}
TY  - JOUR
AU  - Zinovy Reichstein
AU  - Angelo Vistoli
TI  - A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
JO  - Journal of the European Mathematical Society
PY  - 2013
SP  - 1999
EP  - 2026
VL  - 15
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/411/
DO  - 10.4171/jems/411
ID  - JEMS_2013_15_6_a0
ER  - 
%0 Journal Article
%A Zinovy Reichstein
%A Angelo Vistoli
%T A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
%J Journal of the European Mathematical Society
%D 2013
%P 1999-2026
%V 15
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/411/
%R 10.4171/jems/411
%F JEMS_2013_15_6_a0
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. http://geodesic.mathdoc.fr/articles/10.4171/jems/411/

Cité par Sources :