Let pi: \bar{M_{g,1}} \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_*(ω). 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?

`M_g`

, in the title. – Ilya Nikokoshev Oct 22 '09 at 22:18