广义秩小于或等于4的斜对称形式的稳定线性系
Stable linear systems of skew-symmetric forms of generic rank less than or equal to 4
摘要：
给定一个6维复向量空间$W$，我们考虑W上斜对称形式的线性系。这类$n$ -维线性系，也可以解释为$\mathbb{P}(\bigwedge^2 W^*)$的$n$ -维线性子空间，由射影空间$\mathbb{P}(\mathbb{C}^{n+1}\otimes \bigwedge ^2 W^*)$参数化.我们分析了$SL(W)$在这个射影空间上的作用以及线性系关于这个作用的GIT稳定性。我们提出了一个分类的所有稳定轨道的线性系，其通用元素是一个张量的秩为4。
英文摘要：
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.
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