发表机构
Universidade Estadual de Campinas (UNICAMP); Institute for Advanced Studies in Basic Sciences (IASBS); Universidade Federal de São Paulo (UNIFESP); Universidade Federal de Sergipe（坎皮纳斯州立大学; 基础科学高等研究院; 圣保罗联邦大学; 塞尔希培联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三生成齐次理想的数值不变量，推广Bourbaki度并建立尖锐数值界，应用于奇异四次平面曲线，确定其可能Bourbaki度为0,1,2,3,4,6,7,8。
AI 中文摘要
我们研究了由三个形式生成的齐次理想的数值不变量，特别关注合冲模的初始次数、理想的余维二部分的多样性以及Bourbaki度之间的相互作用。我们将Bourbaki度从平面曲线的梯度理想推广到任意三生成齐次理想，并在一般和等生成两种情形下获得了尖锐的数值界。在等生成情形下，这些界扩展了du Plessis–Wall图景，并引出了对数值、结构、维数和可积间隙的研究。我们证明了数值可容许性一般不蕴含可实现性，并从极小分次自由分解中获得进一步限制。作为应用，我们确定了约化奇异四次平面曲线的可能Bourbaki度，并根据其奇点构型加以描述；可能值为0,1,2,3,4,6,7,8。
英文摘要
We study numerical invariants of homogeneous ideals generated by three forms, with particular emphasis on the interaction between the initial degree of the syzygy module, the multiplicity of the codimension-two part of the ideal, and the Bourbaki degree. We extend the Bourbaki degree from gradient ideals of plane curves to arbitrary three-generated homogeneous ideals and obtain sharp numerical bounds in both the general and the equigenerated settings. In the equigenerated case, these bounds extend the du Plessis--Wall picture and lead to the study of numerical, structural, dimensional, and integrable gaps. We show that numerical admissibility does not in general imply realizability and obtain further restrictions from the minimal graded free resolution. As an application, we determine the possible Bourbaki degrees of reduced singular quartic plane curves and describe them in terms of their singularity configurations; the possible values are 0,1,2,3,4,6,7,8.
Comments43 pages. Comments are welcomed
