论文标题
确定性品种的代数矩阵的结果
Results on the algebraic matroid of the determinantal variety
论文作者
论文摘要
我们取得了进展，以表征由变量矩阵的固定大小的未成年人定义的决定性品种的代数矩阵。我们的主要结果是一个新型的基本基库系列，该家族在特殊情况下是矩阵的特征。我们的方法取决于我们介绍的链接匹配领域的放松支持的组合概念，即我们对从参赛作品的一部分完成有限等级的矩阵矩阵的解释，这是Grassmannian上的线性截面问题，以及我们在Sturmfels和Zelelvinsky中用一类Grassmannian所描述的当地坐标和Zelelmfelskins中的一类坐标。
We make progress towards characterizing the algebraic matroid of the determinantal variety defined by the minors of fixed size of a matrix of variables. Our main result is a novel family of base sets of the matroid, which characterizes the matroid in special cases. Our approach relies on the combinatorial notion of relaxed supports of linkage matching fields that we introduce, our interpretation of the problem of completing a matrix of bounded rank from a subset of its entries as a linear section problem on the Grassmannian, and a connection that we draw with a class of local coordinates on the Grassmannian described by Sturmfels and Zelevinsky in 1993.
