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

Zinovy Reichstein; Angelo Vistoli

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 6, page 1999-2026
- ISSN: 1435-9855

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topReichstein, 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 -

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