发表机构
New Mexico State University（新墨西哥州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在特征非2的域上研究二次曲线网随四边形构型变化而保持不变的纠缠现象，证明纠缠等价于中点平分条件及平分线场相等，并给出中心轨迹决定网的结论。
AI 中文摘要
二次曲线网可以在生成它的四点构型变化时保持不变。我们研究这一现象在特征不同于 $2$ 的域 ${\mathbb{k}}$ 上的表现。我们允许退化的四边形，由四个不一定不同的点和六条连接线组成，前提是三条边构成一个非退化三角形。四边形的网是通过将其对边对视为二次曲线所生成的束中的定义多项式添加常数而获得的。当两个四边形生成相同的网时，我们称它们为纠缠的。我们证明纠缠等价于一个看似不对称的条件：一个四边形的每条边在该边中点处平分另一个四边形。网中的线对成员形成一个平分线场，该场决定整个网，因此纠缠也等价于平分线场的相等。最后，我们证明网中中心二次曲线的中心轨迹，连同一条非平行的线对成员，决定整个网。
英文摘要
A net of conics can remain unchanged as the four-point configuration generating it varies. We study this phenomenon over a field ${\mathbb{k}}$ of characteristic different from $2$. We allow degenerate quadrangles, consisting of four not necessarily distinct points and six joining lines, provided that three sides form a nondegenerate triangle. The net of a quadrangle is obtained by adjoining constants to the defining polynomials in the pencil generated by its pairs of opposite sides, viewed as conics. We call two quadrangles entangled when they generate the same net. We prove that entanglement is equivalent to the apparently asymmetric condition that every side of one quadrangle bisects the other quadrangle at that side's midpoint. The line-pair members of the net form a bisector field that determines the entire net, so entanglement is also equivalent to equality of bisector fields. Finally, we prove that the locus of centers of the central conics in the net, together with one nonparallel line-pair member, determines the net.
Comments29 pages, 9 figures. Comments welcome!
