A note on the very ampleness of complete linear systems on blowings-up of P3
Abstract
In this note we consider the blowing-up X of P3 along r general points of the anticanonical divisor of a smooth quadric in P3. Given a complete linear system |L| = |dH - m1 E1 -...- mr Er| on X, with H the pull-back of a plane in P3 and Ei the exceptional divisor corresponding to Pi, we give necessary and sufficient conditions for the very ampleness (resp. base point freeness and non-speciality) of L. As a corollary we obtain a sufficient condition for the very ampleness of such a complete linear system on the blowing-up of P3 along r general points.
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