Base locus of linear systems on the blowing-up of ℙ<sup>3</sup>along at most 8 general points

Volder, Cindy De; Laface, Antonio

doi:10.2140/pjm.2006.223.17

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2014

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“…If r ≤ 8, the points P i are in general position on P 3 and the dimension and base locus of L on X can be determined using the results from [5,6].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A note on the very ampleness of complete linear systems on blowings-up of P3

Ciliberto¹,

Geramita²,

Harbourne³

et al. 2005

Projective Varieties With Unexpected Properties

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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 − · · · − mrEr| 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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“…If r ≤ 8, the points P i are in general position on P 3 and the dimension and base locus of L on X can be determined using the results from [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…The techniques used in this note are a generalization of the ones in [5,6] and make use of the results about complete linear systems on rational surfaces with irreducible anticanonical divisor (see [7,8]). …”

Section: Introductionmentioning

confidence: 99%