The Equations of Space Curves on a Quadric
نویسنده
چکیده
The goal of this note is to study the equations of a curve C ⊂ P3 = PK that is contained in some quadric Q. By a curve, we mean a pure one-dimensional locally Cohen-Macaulay subscheme (i.e. without zero-dimensional components.) We assume that the field K is algebraically closed. If C ⊂ Q is arithmetically Cohen-Macaulay, then, by Dubreil’s Theorem, C is defined by at most 3 equations. The converse is also true by a well-known result of Evans and Griffith ([4, Theorem 2.1]). Denoting by μ(IC) the number of minimal generators of the homogeneous ideal of C, this gives:
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تاریخ انتشار 2005