论文标题
Segre品种的线性依赖子集
Linear dependent subsets of Segre varieties
论文作者
论文摘要
我们研究有限子集的线性代数$ s $ segre品种$ x $。特别是，我们将对$（s，x）$与$ s $ linear依赖性和$ \＃（s）\ le 5 $分类。我们考虑了线性依赖集的附加条件（它们的两个点没有包含在$ x $的行中），并且在$ \＃（s）$的$ \＃（s）$方面的下限和$ x $的因子数量中获得了更好的下限。在此讨论中以及在情况的分类中，$ \＃（s）= 5 $，$ x \ cong \ mathbb {p}^1 \ times \ times \ mathbb {p}^1 \ times \ times \ times \ mathbb {p}^1 $我们使用合理正常曲线
We study the linear algebra of finite subsets $S$ of a Segre variety $X$. In particular we classify the pairs $(S,X)$ with $S$ linear dependent and $\#(S)\le 5$. We consider an additional condition for linear dependent sets (no two of their points are contained in a line of $X$) and get far better lower bounds for $\#(S)$ in term of the dimension and number of the factors of $X$. In this discussion and in the classification of the case $\#(S)= 5$, $X\cong \mathbb {P}^1\times \mathbb {P}^1\times \mathbb {P}^1$ we use the rational normal curves
