论文标题
单一理想的免费分辨率的线性
Linearity of Free Resolutions of Monomial Ideals
论文作者
论文摘要
我们研究具有线性表现或部分线性分辨率的单一理想。我们为3度3的无方便理想以及分辨率是线性的主要理想的线性表现的组合表征，除了最后一步（“几乎是线性”案例）。在某些情况下，我们还对Castelnuovo-Mumford的规律性和发电机数量提高了尖锐的范围。 这是一个基本的观察，即线性属性是通过将理想限制到一个变量子集的限制来遗传的，我们研究了匡威何时保持。我们构建了几乎线性主要理想的分形示例，与Sierpiński三角形相对较少的发生器。我们的结果还导致了高度连接的简单复合物$δ$，这些$δ$无法通过壳上的同一变量扩展到单纯形的完整$ \ dimδ$ - 骨骼。
We study monomial ideals with linear presentation or partially linear resolution. We give combinatorial characterizations of linear presentation for square-free ideals of degree 3, and for primary ideals whose resolutions are linear except for the last step (the "almost linear" case). We also give sharp bounds on Castelnuovo-Mumford regularity and numbers of generators in some cases. It is a basic observation that linearity properties are inherited by the restriction of an ideal to a subset of variables, and we study when the converse holds. We construct fractal examples of almost linear primary ideals with relatively few generators related to the Sierpiński triangle. Our results also lead to classes of highly connected simplicial complexes $Δ$ that can not be extended to the complete $\dim Δ$-skeleton of the simplex on the same variables by shelling.
