Deformations of half-canonical Gorenstein curves in codimension four

2022/11/01 by Ablett, Patience, Coughlan, Stephen
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.00487

Abstract

Recent work of Ablett arXiv:2112.03400 and Kapustka, Kapustka, Ranestad, Schenck, Stillman and Yuan arXiv:2111.05817 outlines a number of constructions for singular Gorenstein codimension four varieties. Earlier work of Coughlan, Gołȩbiowski, Kapustka and Kapustka arXiv:1609.01195 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.

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