La methode d'Horace pour l'interpolation à plusieurs variables (Q1061791)

Here the author considers several maximal rank type problems for zero- dimensional subschemes of \({\mathbb{P}}^ n\). He rises several conjectures and develops a general method to attack them. He applies his method in particular cases. For instance he shows for \(k=2\), \(t=2\) or 3 and for \(k=3\), \(t=2\), at how many general points it is possible to prescribe values and derivatives up to order t-1 to a polynomial of given degree in k variables. The proofs use modern projective geometry (Hilbert schemes, semicontinuity) and a very refined inductive procedure.