论文标题
在线性品种及其热带化中的编态度 - 一个子空间的模量空间
Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization
论文作者
论文摘要
我们研究了固定$（d+1）$ - 尺寸线性品种$ x $的$ D $维线性子空间的模量空间。我们证明这些模量空间是线性子空间本身，因此它们的热带化完全由它们相关的（有价值的）矩形决定。我们表明，这些矩形可以解释为与$ x $相对应的超平面布置线的矩形，并且通常等于自由矩阵的dilworth截断。通过这种方式，我们可以描述一个稳定的稳定地图$ 1 $ $ 1 $的稳定地图的模量空间的对热带的FANO方案和热带化。
We study the moduli space of $d$-dimensional linear subspaces contained in a fixed $(d+1)$-dimensional linear variety $X$, and its tropicalization. We prove that these moduli spaces are linear subspaces themselves, and thus their tropicalization is completely determined by their associated (valuated) matroids. We show that these matroids can be interpreted as the matroid of lines of the hyperplane arrangement corresponding to $X$, and generically are equal to a Dilworth truncation of the free matroid. In this way, we can describe combinatorially tropicalized Fano schemes and tropicalizations of moduli spaces of stable maps of degree $1$ to a plane.
