Generic doublings of almost complete intersections of codimension 3

TL;DR

This paper explores the structure of Gorenstein ideals of codimension 4 derived from generic doublings of almost complete intersection ideals of codimension 3, focusing on their spinor coordinates and module properties.

Contribution

It introduces a new approach to constructing Gorenstein ideals of codimension 4 from codimension 3 ideals and analyzes their conormal and normal modules, including spinor coordinate aspects.

Findings

Characterization of Gorenstein ideals from generic doublings

Analysis of spinor coordinates with 8 and 9 generators

Properties of conormal and normal modules for these ideals

Abstract

We study Gorenstein ideals of codimension $4$ derived from generic doublings of almost complete intersection perfect ideals of codimension $3$. We also investigate spinor coordinates of such Gorenstein ideals with $8$ and $9$ generators. For an ideal $J$ of commutative ring $R$, the $R/J$ module $J/J^2$ is called conormal module and $R/J$-dual of $J/J^2$ is called normal module. We study properties of conormal and normal modules of almost complete intersection perfect ideals of codimension $3$.