Symbolic powers of ideals of generic points in P^3

Abstract

B. Harbourne and C. Huneke conjectured that for any ideal $I$ of fat points in $P^N$ its $r$-th symbolic power $I^{(r)}$ should be contained in $M^{(N-1)r}{I}^r$, where $M$ denotes the homogeneous maximal ideal in the ring of coordinates of $P^N$. We show that this conjecture holds for the ideal of any number of simple (not fat) points in general position in $P^3$ and for at most $N+1$ simple points in general position in $P^N$. As a corollary we give a positive answer to Chudnovsky Conjecture in the case of generic points in $P^3$.

References in corpus (1)

• Regularity and non-emptyness of linear systems in ${\mathbb{P}}^n$

Cited by in corpus (1)

• Containments of symbolic powers of ideals of generic points in $\PP^3$