论文标题
帕斯卡线的退化
Degenerations of Pascal Lines
论文作者
论文摘要
令$ \ Mathcal {k} $表示复杂的投影平面中的非单词圆锥。帕斯卡（Pascal）的定理说，在$ \ mathcal {k} $上的六个不同的点$ a，b，c，d，e，f $，三个相交点$ ae \ cap bf，ad \ cap cf，bd \ cap ce $是共线。包含它们的线称为六分线的帕斯卡线。但是，当六个点中的某些人汇集时，这种结构可能会失败。在本文中，我们发现帕斯卡线未明确定义的不确定性基因座，然后使用沿多核对角线进行爆炸来定义它。我们在这些退化的情况下分析了PASCALS的几何形状。最后，我们提供了一些关于帕斯卡（Pascal）hexagrammum mysticum中其他几何元素不确定性的评论。
Let $\mathcal{K}$ denote a nonsingular conic in the complex projective plane. Pascal's theorem says that, given six distinct points $A,B,C,D,E,F$ on $\mathcal{K}$, the three intersection points $AE \cap BF, AD \cap CF, BD \cap CE$ are collinear. The line containing them is called the Pascal line of the sextuple. However, this construction may fail when some of the six points come together. In this paper, we find the indeterminacy locus where the Pascal line is not well-defined and then use blow-ups along polydiagonals to define it. We analyse the geometry of Pascals in these degenerate cases. Finally we offer some remarks about the indeterminacy of other geometric elements in Pascal's hexagrammum mysticum.
