Gorenstein liaison of curves in \(\mathbb{P}^4\)
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.
Gorenstein-linked to a complete intersection
scientific article; zbMATH DE number 1512983