Essential dimension and algebraic stacks

Details Essential dimension and algebraic stacks Essential dimension and algebraic stacks

2007-01-31

arxiv.org/abs/math/0701903v1

Mathematics

Algebraic Geometry

52 pages

Scientific paper

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.

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