论文标题
丰富的Wronski程度
An enriched degree of the Wronski
论文作者
论文摘要
给定$ MP $不同的$ p $ - 平面在$（m+p）$ - 尺寸空间中，一个经典的问题是询问有多少$ p $ - 平面相交。例如，当$ m = p = 2 $时，这正是在项目启动后“在3个空间中符合四行”的问题。 Wronski地图的Brouwer程度为这个一般问题提供了一个答案，该问题首先是由Schubert计算的，关于复数，Eremenko和Gabrielov对Reals进行了计算。我们使用$ \ mathbf {a}^1 $ - homotoppy理论的机械提供了所有$ m $和$ p $的富含wronski的wronski。我们进一步证明，在所有奇偶族中，$ m $平面的本地贡献是与$ p $平面相交的某些plücker坐标之间的决定性关系。
Given $mp$ different $p$-planes in general position in $(m+p)$-dimensional space, a classical problem is to ask how many $p$-planes intersect all of them. For example when $m = p = 2$, this is precisely the question of "lines meeting four lines in 3-space" after projectivizing. The Brouwer degree of the Wronski map provides an answer to this general question, first computed by Schubert over the complex numbers and Eremenko and Gabrielov over the reals. We provide an enriched degree of the Wronski for all $m$ and $p$ even, valued in the Grothendieck-Witt ring of a field, using machinery from $\mathbf{A}^1$-homotopy theory. We further demonstrate in all parities that the local contribution of an $m$-plane is a determinantal relationship between certain Plücker coordinates of the $p$-planes it intersects.
