English

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.

Keywords

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