  We show that the Masur-Veech volumes and area Siegel-Veech constants can be
obtained by intersection numbers on the strata of Abelian differentials with
prescribed orders of zeros. As applications, we evaluate their large genus
limits and compute the saddle connection Siegel-Veech constants for all strata.
We also show that the same results hold for the spin and hyper-elliptic
components of the strata.
