三个变量中余维 $2$ 的线性展示完全理想
交换代数
2017-12-07 v3 代数几何
摘要
本文的目标是标题中所述理想的精细结构，重点在于相关的 Rees 代数和特殊纤维的性质。本方法与文献中某些先前工作的分水岭在于，此处不假设所讨论的理想满足常见的泛型性质。唯一的例外是近期 N. P. H. Lan 的工作启发了本文。在此我们复原并扩展了该工作。我们强烈关注相应的所谓 Hilbert--Burch 矩阵的子式理想的行为以及后者的共轭特征。我们将结果应用于三个重要模型：平面胖点的线性展示理想、超平面排列的倒数理想以及线性展示单项理想。
引用
@article{arxiv.1709.02633,
title = {Linearly presented perfect ideals of codimension $2$ in three variables},
author = {André Dória and Zaqueu Ramos and Aron Simis},
journal= {arXiv preprint arXiv:1709.02633},
year = {2017}
}
备注
32 pages. This is a revised version. The introduction has been extensively modified. Section 2 was modified and one of the main results was further detailed. We include new bibliographical references