论文标题
偏斜形式的通用等级的稳定线性系统小于或等于4
Stable linear systems of skew-symmetric forms of generic rank less than or equal to 4
论文作者
论文摘要
给定6维复杂的矢量空间$ W $，我们考虑W. $ n $二维线性系统的偏斜形式形式的线性系统，也可以解释为$ n $ dimensional-demensional-demensional线性子空间$ \ Mathbb {p}（P}（\ BigWedge^2 W^*）$，parjientive projivesive projivesive projivesive space $ \ mathbb {p}（\ Mathbb {c}^{n+1} \ otimes \ bigWedge^2 w^*）$。我们分析了此投影空间上的$ SL（W）$动作以及有关此操作的线性系统的GIT稳定性。我们提出了所有稳定轨道的线性系统的分类，其通用元素是等级4的张量。
Given a 6-dimensional complex vector space $W$, we consider linear systems of skew-symmetric forms on W. The $n$-dimensional linear systems this kind, that can also be interpreted as $n$-dimensional linear subspaces of $\mathbb{P}(\bigwedge^2 W^*)$, are parametrized by the projective space $\mathbb{P}(\mathbb{C}^{n+1}\otimes \bigwedge ^2 W^*)$. We analyze the $SL(W)$ action on this projective space and the GIT stability of linear systems with respect to this action. We present a classification of all stable orbits of linear systems whose generic element is a tensor of rank 4.
