A vanishing theorem and symbolic powers of planar point ideals
arXiv:1302.0871 · doi:10.1112/S1461157013000181
Abstract
The purpose of this note is twofold. We present first a vanishing theorem for families of linear series with base ideal being a fat points ideal. We apply then this result in order to give a partial proof of a conjecture raised by Bocci, Harbourne and Huneke concerning containment relations between ordinary and symbolic powers of planar point ideals.
17 pages