A note on the very ampleness of complete linear systems on blowings-up of P^3
Algebraic Geometry
2007-05-23 v1
Abstract
In this note we consider the blowing-up X of P^3 along r general points of the anticanonical divisor of a smooth quadric in P^3. Given a complete linear system |L| = |dH - m_1 E_1 -...- m_r E_r| on X, with H the pull-back of a plane in P^3 and E_i the exceptional divisor corresponding to P_i, 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 P^3 along r general points.
Cite
@article{arxiv.math/0409526,
title = {A note on the very ampleness of complete linear systems on blowings-up of P^3},
author = {Cindy De Volder and Antonio Laface},
journal= {arXiv preprint arXiv:math/0409526},
year = {2007}
}
Comments
6 pages, LaTeX