Cindy De Volder, Antonio Laface
Published 2004-09-27Version 1
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.
Base locus of linear systems on the blowing-up of P^3 along at most 8 general points
Varieties Connected by Chains of Lines
Cones of divisors on $\mathbb{P}^3$ blown up at eight very general points
![QR code for arXiv:math/0409526 [math.AG]](http://oss.arxitics.com/images/favicon.svg)