On the effective cone of (P^n) blown-up at (n+3) points

We start with an overview on Interpolation Problems. In particular, we study linear systems of hypersurfaces of a fixed degree passing through a collection of (n+3) general points with assigned multiplicities.
We prove that the rational normal curve of degree n passing through the points, its secant varieties and joins with linear subspaces are cycles of their base locus and we compute their multiplicity.
This yelds a conjectural formula for the dimension of such linear systems, completing a conjecture in the commutative algebra setting due to Froeberg-Iarrobino. We compute the facets of the effective and movable cones of divisors on blown-up projective spaces.

This is joint work with M. C. Brambilla and E. Postinghel

Referente: Marco Andreatta