Essential dimension and algebraic stacks

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.

52 pages

References in corpus (1)

• Essential dimensions of finite groups

Cited by in corpus (5)

• The behavior of essential dimension under specialization
• Upper bounds for the essential dimension of the moduli stack of ${\sl_{n}}$-bundles over a curve
• The genericity theorem for the essential dimension of tame stacks
• Incompressibility of orthogonal Grassmannians of rank 2
• Essential dimension of the moduli stack of polarized K3 surfaces