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Arithmetically normal sheaves. (English) Zbl 0639.14008

The author defines an arithmetically normal sheaf on the projective space \({\mathbb{P}}^ 3\) as a rank 2 reflexive sheaf \({\mathcal F}\) such that \((i)\quad H^ 1({\mathcal F}(n))=0\) for all integers n, and (ii), if \({\mathcal F}(s)\) is globally generated, the zero scheme of its general section is a smooth curve. For a suitable twist, the sections of such a sheaf define arithmetically normal curves. If \({\mathcal F}\) satisfies only condition (ii), it is said to be curvilinear. Using this notion the author states some results on the existence of curvilinear sheaves such that for every \(n\geq -2[c_ 1({\mathcal F})/2]\) at most one group \(H^ i({\mathcal F}(n))\) is different from zero.
Reviewer: I.Dolgachev

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14N05 Projective techniques in algebraic geometry
14H99 Curves in algebraic geometry
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References:

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