LAUSR

We completely determine the intersection cohomology of the Satake compactifications $${{\mathcal {A}}_{2}^{\mathrm{Sat}}},{{\mathcal {A}}_{3}^{\mathrm{Sat}}}$$A2Sat,A3Sat, and $${{\mathcal {A}}_{4}^{\mathrm{Sat}}}$$A4Sat, except for $${ IH}^{10}({{\mathcal {A}}_{4}^{\mathrm{Sat}}})$$IH10(A4Sat). We also determine all the ingredients appearing in the decomposition theorem applied to the map from a toroidal compactification to the Satake compactification in these genera. As a byproduct we obtain in addition several results about the intersection cohomology of the link bundles involved.