Deformations of arithmetically Cohen-Macaulay subvarieties of \({\mathbb{P}}^ n\)
In this short note the authors show that every arithmetically Cohen- Macaulay 2-codimensional subscheme of \({\mathbb{P}}^ N\) can be deformed to a (reduced) union of 2-codimensional linear subvarieties. This extends an old result of E. Gaeta \((N=3)\) to the higher dimensional case. The authors make use of linkage techniques.
deformation of arithmetically Cohen-Macaulay varieties
scientific article; zbMATH DE number 4160944
scientific article