Essential dimension and algebraic stacks
Algebraic Geometry
2007-05-23 v1
Abstract
We define and study the essential dimension of an algebraic stack. We compute the essential dimension of the stacks Mgn and MgnBar of smooth, or stable, n-pointed curves of genus g. We also prove a general lower bound for the essential dimension of algebraic groups with a non-trivial center. Using this, we find new exponential lower bounds for the essential dimension of spin groups and new formulas for the essential dimension of some finite p-groups. Finally, we apply the lower bound for spin groups to the theory of the Witt ring of quadratic forms over a field k.
Cite
@article{arxiv.math/0701903,
title = {Essential dimension and algebraic stacks},
author = {Patrick Brosnan and Zinovy Reichstein and Angelo Vistoli},
journal= {arXiv preprint arXiv:math/0701903},
year = {2007}
}
Comments
52 pages