论文标题
满足矩形cayley的曲霉 - 巴哈拉赫的财产和覆盖公寓的等级
Matroids satisfying the matroidal Cayley--Bacharach property and ranks of covering flats
论文作者
论文摘要
令$ m $成为一个矩阵，满足了Cayley-Bacharach条件的矩形类似物。考虑到数字$ k \ ge 2 $，我们表明，覆盖$ m $的基本集合的$ k $ tuple的排名没有非平凡的限制。这解决了一个由较早的结果激励的莱文森破产问题的问题，该问题表明，满足Cayley-Bacharach条件的点数限制了它们迫使他们躺在低维线性子空间上。我们还探讨了一个普遍的问题，是什么矩形满足给定程度的基质卡利 - 巴哈拉赫条件，及其与广义的permutohedra和Graphic Matroids的几何形状的关系。
Let $M$ be a matroid satisfying a matroidal analogue of the Cayley-Bacharach condition. Given a number $k \ge 2$, we show that there is no nontrivial bound on ranks of a $k$-tuple of flats covering the underlying set of $M$. This addresses a question of Levinson-Ullery motivated by earlier results which show that bounding the number of points satisfying the Cayley-Bacharach condition forces them to lie on low-dimensional linear subspaces. We also explore the general question what matroids satisfy the matroidal Cayley-Bacharach condition of a given degree and its relation to the geometry of generalized permutohedra and graphic matroids.
