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 -
