Title: Linear obstructions for linear systems in P^n

The linear system L of degree-d hypersurfaces of P^n with prescribed 
general multiple points is said to be special if the conditions 
imposed by the multiple points are not linearly independent. This 
phenomenon occurs when the multiplicities force L to contain in its 
base locus higher dimensional cycles. We will discuss the case when 
such cycles are linear and introduce the notion of linear speciality, 
which provides a geometric interpretation of algebraic conjectures 
by Fröberg and Iarrobino on the Hilbert function of ideals generated 
by powers of general linear forms.

This is joint work with M. C. Brambilla and O. Dumitrescu.