Extending Infinitely Many Times Arithmetically Cohen–Macaulay and Gorenstein Subvarieties of Projective Spaces

Abstract

We give examples of infinitely extendable (not as cones) arithmetically Cohen–Macaulay and arithmetically Gorenstein subvarieties of projective spaces and which are not complete intersections. The proof uses the computation of the dimension of the Hilbert scheme of codimension 2 subschemes of projective spaces due to G. Ellingsrud and of arithmetically Gorenstein codimension 3 subschemes due to J. O. Kleppe and R.-M. Miró-Roig.