论文标题
在$ \ mathbb r^3 $中的线和圆的交叉点数上
On the number of intersection points of lines and circles in $\mathbb R^3$
论文作者
论文摘要
我们考虑以下问题：给定的$ n $行和$ n $ circled in $ \ mathbb {r}^3 $，在至少一条线上以及至少一个家庭中的一个圆圈上的交点的最大数量是多少。我们证明，如果没有$ n^{1/2} $ curves（线或圆圈）位于学位表面上最多两个，那么这些相交点的数量为$ O（n^{3/2}）$。
We consider the following question: Given $n$ lines and $n$ circles in $\mathbb{R}^3$, what is the maximum number of intersection points lying on at least one line and on at least one circle of these families. We prove that if there are no $n^{1/2}$ curves (lines or circles) lying on an algebraic surface of degree at most two, then the number of these intersection points is $O(n^{3/2})$.
