论文标题
具有系数的标志矩阵
Flag matroids with coefficients
论文作者
论文摘要
本文是对贝克 - 鲍勒理论的直接概括来标记矩形，包括贝克（Baker）开发的模量解释和Matroids的第二作者。更明确的是，我们将国旗矩阵的概念扩展到任何区域上的标志成型原子体，从基础公理（Grassmann-Plücker函数），电路/矢量公理和二重对方面提供隐态描述，包括在完美的情况下进行其他特征。我们建立了标志矩形的双重性并建造未成年人。基于有序的蓝色方案理论，我们引入了标志矩阵束并构建其模量空间，从而导致对偶性和未成年人的代数几何描述。采用合理点在几种几何环境中恢复了标志品种：在（拓扑）字段，热带几何形状以及作为MacPhersonian的概括中。
This paper is a direct generalization of Baker-Bowler theory to flag matroids, including its moduli interpretation as developed by Baker and the second author for matroids. More explicitly, we extend the notion of flag matroids to flag matroids over any tract, provide cryptomorphic descriptions in terms of basis axioms (Grassmann-Plücker functions), circuit/vector axioms and dual pairs, including additional characterizations in the case of perfect tracts. We establish duality of flag matroids and construct minors. Based on the theory of ordered blue schemes, we introduce flag matroid bundles and construct their moduli space, which leads to algebro-geometric descriptions of duality and minors. Taking rational points recovers flag varieties in several geometric contexts: over (topological) fields, in tropical geometry, and as a generalization of the MacPhersonian.
