2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/123059We 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 pagesAlgebraic Geometry14A20; 20G15; 11E04; 14H10text