Using the concept of d-collapsibility from combinatorial topology, we define chordal simplicial complexes and show that their Stanley-Reisner ideals are componentwise linear. Our construction is inspired by and an extension of “chordal clutters” which was defined by Bigdeli, Yazdan Pour and Zaare-Nahandi in 2017, and characterizes Betti tables of all ideals with a linear resolution in a polynomial ring.

We show d-collapsible and d-representable complexes produce componentwise linear ideals for appropriate d. Along the way, we prove that there are generators that when added to the ideal, do not change Betti numbers in certain degrees.

We then show that large classes of componentwise linear ideals, such as Gotzmann ideals and square-free stable ideals have chordal Stanley-Reisner complexes, that Alexander duals of vertex decomposable complexes are chordal, and conclude that the Betti table of every componentwise linear ideal is identical to that of the Stanley-Reisner ideal of a chordal complex.

使用组合拓扑中的d-可折叠性概念，我们定义了弦简单复形，并表明它们的Stanley-Reisner理想是分量线性的。我们的构造受到Bigdeli，Yazdan Pour和Zaare-Nahandi在2017年定义的“弦杂波”的启发和扩展，并用多项式环中的线性分辨率表征了所有理想的贝蒂表。

我们证明了d可折叠和d表示的复合物对于适当的d产生分量线性理想。一路走来，我们证明了有一些生成器在添加到理想状态时不会在一定程度上更改贝蒂数。

然后，我们证明了大类的成分线性理想，例如Gotzmann理想和无平方稳定理想具有弦的Stanley-Reisner复数，顶点可分解复合物的Alexander对偶是弦的，并得出结论，每个分量线性理想的Betti表是与Stanley-Reisner理想的弦乐复合体相同。