On the postulation of sᵈ fat points in Pᵈ

الأصل · EN

In connection with his counter-example to the fourteenth problem of Hilbert, Nagata formulated a conjecture concerning the postulation of r fat points of the same multiplicity in the projective plane and proved it when r is a square. Iarrobino formulated a similar conjecture in any projective space Pᵈ. We prove Iarrobino's conjecture when r is a d-th power. As a corollary, we obtain new counter-examples modeled on those by Nagata.