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Construction of space curves with good properties. (English) Zbl 0693.14018

We show that for all (d,g) in the degree, genus plane which are between a certain piecewise linear curve \(C_ K\) of order \(g\sim \frac{2\sqrt{2}}{3}d^{3/2}\) and a curve \(C_ 1\) of order \(g\sim \frac{2}{3}d^{3/2}\), there are smooth connected curves with degree d and genus g which are of maximal rank.
We also show that for all (d,g) between the curve \(C_ K\) and the d- axis, there are smooth connected curves Y with degree d and genus g such that \(h^ 1I_ Y(n)\cdot h^ 2I_ Y(n)=0\) for all \(n\in {\mathbb{Z}}\). Together with a previous result of Sernesi this implies that for all (d,g) in this area there are components \(H_{d,g}\) of the Hilbert scheme with the expected number of moduli.
Reviewer: G.Fløystad

MSC:

14H50 Plane and space curves
14N05 Projective techniques in algebraic geometry
14C05 Parametrization (Chow and Hilbert schemes)
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References:

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