Joint work with Joint work with Carlos Rito and Alessandra Sarti.

Using smoothing technics, Schoen constructed a family of surfaces S with K^2=2, c_2=16, q=4, which have many remarkable properties.

In a previous work with C. Ciliberto and M. Mendes-Lopes, we proved that a Schoen surface S are double cover of a degree 8 complete intersection surface in P^4 with 40 nodes (which is the maximal number possible).

In this talk we construct  in an effective way a degree 8 complete intersection surface Z in P^4 with 40 nodes, using the geometries of quartic K3 surfaces with 15 nodes, the Segre cubic threefold and the Igusa quartic threefold.

A double cover S of Z branched over the 40 nodes has the same invariants as the Schoen surface S and we prove that it is not isogeneous to a higher quotient. We then exhibit an example of a surface Sâ with maximal Picard number and a large group of symmetries.