  Motivated by our study (elsewhere) of linear syzygies of homogeneous ideals
generated by quadrics and their restrictions to subvarieties of the ambient
projective space, we investigate in this note possible zero-dimensional
intersections of two Veronese surfaces in P^5.
  The case of two Veronese surfaces in P^5 meeting in 10 simple points appears
also in work of Coble, Conner and Reye in relation to the 10 nodes of a quartic
symmetroid in P^3, and we provide here a modern account for some of their
results.
