TITLE: Reference for the Hodge Bundle
QUESTION [9 upvotes]: For the purposes of this question, let the Hodge bundle $\lambda$ be the bundle on a fibration of abelian varieties $X\to B$ with fiber over $b\in B$ the space of 1-forms on $X_b$, or the pullback to $B$ along the zero section of the sheaf of relative differentials.  The most interesting examples are when $B$ is $M_g$ or $A_g$, and the fibrations are the Jacobian fibration or the universal family of abelian varieties.
Is there a good reference for the properties of this bundle? And for the determinant line bundle on these spaces? Things like self-intersection numbers, cohomology (in particular global sections) are particularly of interest.

REPLY [4 votes]: The list of references is way too long. Here are some classical texts containing both the setup and calculations:
1) P. Deligne, Le déterminant de la cohomologie, Current Trends in Arithmetical Algebraic Geometry, Contemp. Math., no. 67, AMS, Providence, 1987.
2) Gerd Faltings, Ching-Li Chai, Degenerations of abelian varieties, Springer-Verlag, 1990.
3) L. Moret-Bailly, Pinceaux de variétés abéliennes, Astérisque 129 (1985).
And here are a couple of more recent papers that deal with the self-intersection and cohomology calculations:
4) Alexis Kouvidakis, Theta line bundles and the determinant of the Hodge bundle, arXiv:alg-geom/9604017.
5) Alexander Polishchuk, Determinant bundles for abelian schemes, arXiv:alg-geom/9703021.