AI 中文总结
本文针对完全交奇点研究中提出的Buchsbaum–Eisenbud–Horrocks猜想的变体，证明其部分成立、一般情形不成立，并提出该猜想的局部变体。
AI 中文摘要
Buchsbaum–Eisenbud–Horrocks猜想在过去五十年间吸引了众多交换代数与代数几何领域研究者的关注。近期，Lima–Pereira、Nuño–Ballesteros、Orefice–Okamoto和Tomazella在完全交奇点的研究中提出了该猜想的一个变体。本文一方面展示了该猜想成立的若干情形，另一方面通过构造反例证明该猜想在一般情形下不成立，最后提出了可视为Buchsbaum–Eisenbud–Horrocks猜想局部变体的新猜想。
英文摘要
The Buchsbaum--Eisenbud--Horrocks conjecture has attracted the attention of many researchers working in Commutative Algebra and Algebraic Geometry in the last fifty years. Quite recently, a variant of this conjecture has been formulated by Lima--Pereira, Nuño--Ballesteros, Orefice--Okamoto and Tomazella in their study of complete intersection singularities. The purpose of this paper is, on the one hand, to exhibit some cases where this conjecture holds. On the other hand, we show that the conjecture fails in general by exhibiting some counterexamples. Finally, we formulate a conjecture that can be regarded as a local variant of the Buchsbaum--Eisenbud--Horrocks' one.
Comments15 pages, to appear in Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
