论文标题
曲霉的曲霉 - 曲霉和独立性/依赖性的矩形特性的依赖性
Matroidal Cayley-Bacharach and independence/dependence of geometric properties of matroids
论文作者
论文摘要
我们考虑了$ a $ a $ cayley-bacharach属性的矩形类似物（有限的积分，无法对$ a $ a $ a hypersurfaces施加独立条件）和矩阵的几何特性。如果相关的曲霉层是Nestohedra，我们表明最小的曲霉Cayley-Bacharach属性表示为$ MCB（a）$，取决于用于构造它们的建筑集的结构。该分析还适用于其他学位$ a $。而且，它似乎不会影响矩阵多层的组合等效类别。 但是，与最小的非平凡度$ a $ a $的连接以及有关铺路矩阵的矩形的几何形状（在给定等级的矩形之间是构想通用的）和由超透明增生平面布置构建的。铺路曲霉的情况仍然与建筑集的特性有关，因为它与（希尔伯特（Hilbert）系列）曲面的（希尔伯特（Hilbert）系列）密切相关，这是奇妙的紧凑型共同体的组合模型。最后，我们对可覆盖线和超平面排列的分析给出了一个与点一平面曲线施加的独立性条件或可以递归分析的成曲子家族。
We consider the relationship between a matroidal analogue of the degree $a$ Cayley-Bacharach property (finite sets of points failing to impose independent conditions on degree $a$ hypersurfaces) and geometric properties of matroids. If the matroid polytopes in question are nestohedra, we show that the minimal degree matroidal Cayley-Bacharach property denoted $MCB(a)$ is determined by the structure of the building sets used to construct them. This analysis also applies for other degrees $a$. Also, it does not seem to affect the combinatorial equivalence class of the matroid polytope. However, there are close connections to minimal nontrivial degrees $a$ and the geometry of the matroids in question for paving matroids (which are conjecturally generic among matroids of a given rank) and matroids constructed out of supersolvable hyperplane arrangements. The case of paving matroids is still related to with properties of building sets since it is closely connected to (Hilbert series of) Chow rings of matroids, which are combinatorial models of the cohomology of wonderful compactifications. Finally, our analysis of supersolvable line and hyperplane arrangements give a family of matroids which are natrually related to independence conditions imposed by points one plane curves or can be analyzed recursively.
