Let pi: \bar{M<sub>g,1</sub>} \to \bar{M\_g} be natural projection of compactified moduli stacks of curves and let omega be the relative dualizing sheaf. Then the Hodge class \lambda of \bar{M\_g} is the first chern class of the pushforward \pi\_\*(&omega;). Among other things the hodge class, together with the boundary divisors, freely generates the Picard group of \bar{M\_g}.

> **Question**: Why is lambda big and nef?