Deformations of half-canonical Gorenstein curves in codimension four

Recent work of Ablett (2021) and Kapustka, Kapustka, Ranestad, Schenck, Stillman and Yuan (2021) outlines a number of construc-tions for singular Gorenstein codimension four varieties. Earlier work of Coughlan, Gole,biowski, Kapustka and Kapustka (2016) details a series of nonsingular Gorenstein codimension four con-structions with different Betti tables. In this paper we exhibit a number of flat deformations between Gorenstein codimension four varieties in the same Hilbert scheme, realising many of the singular varieties as specialisations of the earlier nonsingular varieties.& COPY; 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).