Gorenstein liaison of curves in \(\mathbb{P}^4\). (English) Zbl 0983.14035
In studying Gorenstein liaison (a generalization in higher codimension of the well-known theory of ordinary liaison in codimension two) a first natural question is if there exists only one equivalence class containing arithmetically Cohen-Macaulay subschemes.
For curves in the projective four-dimensional space, this paper gives a sufficient condition for an arithmetically Cohen-Macaulay subscheme on a “general” arithmetically Cohen-Macaulay surface in order to be Gorenstein-linked to a complete intersection (briefly, glicci). This result is performed by studying the Picard group of arithmetically Cohen-Macaulay surfaces, thus finding a numerical condition on the canonical divisor of their hyperplane sections.
For curves in the projective four-dimensional space, this paper gives a sufficient condition for an arithmetically Cohen-Macaulay subscheme on a “general” arithmetically Cohen-Macaulay surface in order to be Gorenstein-linked to a complete intersection (briefly, glicci). This result is performed by studying the Picard group of arithmetically Cohen-Macaulay surfaces, thus finding a numerical condition on the canonical divisor of their hyperplane sections.
Reviewer: Giorgio Bolondi (Milano)
MSC:
| 14M06 | Linkage |
| 14H50 | Plane and space curves |
| 14M05 | Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) |
Keywords:
glicci; Picard group; Gorenstein liaison; arithmetically Cohen-Macaulay subscheme; Gorenstein-linked to a complete intersectionReferences:
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