Recent work of Ablett (2021) and Kapustka, Kapustka, Ranestad, Schenck, Stillman and Yuan (2021) outlines a number of constructions for singular Gorenstein codimension four varieties. Earlier work of Coughlan, Gołȩbiowski, Kapustka and Kapustka (2016) details a series of nonsingular Gorenstein codimension four constructions 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.

Ablett ( 2021 ) 和 Kapustka、Kapustka、Ranestad、Schenck、Stillman 和 Yuan ( 2021 )的最新工作概述了奇异 Gorenstein 余维四变体的一些构造。Coughlan、Gołşbiowski、Kapustka 和 Kapustka ( 2016 ) 的早期工作详细介绍了一系列具有不同 Betti 表的非奇异 Gorenstein 余维四结构。在本文中，我们在同一希尔伯特方案中展示了 Gorenstein 余维四变体之间的许多平坦变形，实现了许多奇异变体作为早期非奇异变体的特化。