We propose an upper bound for the regularity index of fat points of P^n with no geometric conditions on the points. Whenever the conjecture is true, the bound is sharp. It is, in fact, reached when there are points with high multiplicities either on a line or an some rational curve. Besides giving an easy proof of the conjecture in P^2, we prove it in P^3, by using some preliminary results which hold, more generally, in P^n.
On a sharp bound for the regularity index of any set of fat points
FATABBI, Giuliana;LORENZINI, Anna
2001
Abstract
We propose an upper bound for the regularity index of fat points of P^n with no geometric conditions on the points. Whenever the conjecture is true, the bound is sharp. It is, in fact, reached when there are points with high multiplicities either on a line or an some rational curve. Besides giving an easy proof of the conjecture in P^2, we prove it in P^3, by using some preliminary results which hold, more generally, in P^n.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
