A genericity theorem for algebraic stacks and essential dimension of hypersurfaces

Reichstein, Zinovy, and Vistoli, Angelo. "A genericity theorem for algebraic stacks and essential dimension of hypersurfaces." Journal of the European Mathematical Society 015.6 (2013): 1999-2026. <http://eudml.org/doc/277345>.

@article{Reichstein2013,
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.},
author = {Reichstein, Zinovy, Vistoli, Angelo},
journal = {Journal of the European Mathematical Society},
keywords = {essential dimension; hypersurface; genericity theorem; stack; gerbe; essential dimension; hypersurface; genericity theorem; stack; gerbe},
language = {eng},
number = {6},
pages = {1999-2026},
publisher = {European Mathematical Society Publishing House},
title = {A genericity theorem for algebraic stacks and essential dimension of hypersurfaces},
url = {http://eudml.org/doc/277345},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Reichstein, Zinovy
AU - Vistoli, Angelo
TI - A genericity theorem for algebraic stacks and essential dimension of hypersurfaces
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 6
SP - 1999
EP - 2026
AB - 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.
LA - eng
KW - essential dimension; hypersurface; genericity theorem; stack; gerbe; essential dimension; hypersurface; genericity theorem; stack; gerbe
UR - http://eudml.org/doc/277345
ER -