Hodge bundle

This is another natural bundle on $\mathcal{M}_{g,n}$; the fibre over a curve $C$ of genus $g$ is the rank $g$ vector space of differentials (holomorphic 1-forms) on $C$. This bundle can be extended naturally to a vector bundle over $\overline{\mathcal{M}}_{g,n}$ by considering certain meromorphic differentials on curves in the boundary.