1988
DOI: 10.1007/bf01389367
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The Hilbert function of generic plane sections of curves of ?3

Abstract: Summary. A characteristic condition is given on a zero-dimensional differentiable 0-sequence H={hi}i_>o, h~<3, in order to be the Hilbert function of a generic plane section of a reduced irreducible curve of ~,3, hence of points of ~,2 with the uniform position property. In this way an answer is given to some question stated by Harris in [Ha2].The result is obtained by constructing a smooth irreducible arithmetically Cohen-Macaulay curve in ~E)3 whose generic plane section has an assigned Hilbert function sati… Show more

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Cited by 47 publications
(24 citation statements)
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“…In these cases, there exists an irreducible smooth aCM curve whose generic plane section has H Z as Hilbert function [14]. So, if C is an integral curve satisfying Theorem 3.9,…”
Section: Theorem 39mentioning
confidence: 99%
“…In these cases, there exists an irreducible smooth aCM curve whose generic plane section has H Z as Hilbert function [14]. So, if C is an integral curve satisfying Theorem 3.9,…”
Section: Theorem 39mentioning
confidence: 99%
“…It has been important, for instance, in the classification and construction of smooth curves in P 3 (e.g. [6], [15], [21], [27]), smooth surfaces in P 4 (e.g. [5], [12], [36], [38]) and smooth threefolds in P 5 (e.g.…”
Section: Linkagementioning
confidence: 99%
“…A precise analog of these results for the integral Gorenstein codimension three case was provided by J. Herzog, N. Trung and G. Valla [17]. From the point of view of the Hilbert function, the necessary and sufficient condition for the existence of smooth aCM curves in P 3 (or irreducible codimension two aCM schemes in P n ) was given by C. Peskine and L. Szpiro [22] and by R. Maggioni and A. Ragusa [19] (see also [13]). This has a precise analog (using Stanley's result above) for integral Gorenstein codimension three schemes, proved by E. De Negri and G. Valla [9].…”
Section: Introductionmentioning
confidence: 88%