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A note on the very ampleness of complete linear systems on blowings-up of P^3

Cindy De Volder·Antonio Laface
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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.

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Cindy De Volder, Antonio Laface. 2004-09-27. A note on the very ampleness of complete linear systems on blowings-up of P^3. https://arxiv.org/abs/math/0409526

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