Elisa Postinghel: Fat points in projective spaces: a geometric approach

We start with an overview on interpolation problems and their translation into the setting of Fröberg-Iarrobino's conjectures. In particular, we study linear systems of hypersurfaces of P^n of fixed degree passing through a collection of n+3 general points with assigned multiplicities.
We show that the linear subspaces spanned by the points, the unique rational normal curve of degree n passing through the n+3 points and its secant varieties are contained with multiplicity in the base locus. This yelds a conjectural formula for the dimension of such linear systems, or equivalentely for the Hilbert series of ideals generated by n+3 powers of linear forms.
This is joint work with M. C. Brambilla and O. Dumitrescu