Ferruccio Orecchia

BIVARIATE HERMITE INTERPOLATION AND LINEAR SYSTEMS OF PLANE CURVES WITH BASE FAT POINTS

. When the multiplicities are all equal,to m say, this problem has been attacked by a number of authors (Lorentz andLorentz, Ciliberto and Miranda, Hirschowitz) and there are a number of goodconjectures (Hirschowitz, Ciliberto and Miranda) on the dimension of these inter-polating spaces. The determination of the dimension has been already solved form ≤ 12 and all d and n by a degeneration technique and some ad hoc geometricarguments. Here this technique is applied up through m = 20; since it fails insome cases, we resort (in these exceptional cases) to the bivariete Hermite interpo-lation with the support of a simple idea suggested by Gr¨obner bases computation.In summary we are able to prove that the dimension of the vector space is theexpected one for 13 ≤ m ≤ 20.