A blocking set in a projective plane is a point set intersecting each line. The smallest blocking sets are lines. The second smallest minimal blocking sets are Baer subplanes (subplanes of order $\sqrt{q}$). Our aim is to study the stability of Baer subplanes in PG$(2,q)$. If we delete $\sqrt{q}+1-k$ points from a Baer subplane, then the resulting set has size $q+k$ and $(\sqrt{q}+1-k)(q-\sqrt{q})$ 0-secants. If we have somewhat more 0-secants, then our main theorem says that this point set can be obtained from a Baer subplane or from a line by deleting somewhat more than $\sqrt{q}+1-k$ points and adding some points. The motivation for this theorem comes from planes of square order, but our main result is valid also for non-square orders. Hence in this case the point set contains a relatively large collinear subset.

投影平面中的遮挡集是与每条线相交的点集。最小的阻塞集是线。第二个最小的最小阻塞集是Baer子平面（次平面$\sqrt{q}$）。我们的目的是研究PG中Baer子平面的稳定性$（2，q）$。如果我们删除$\sqrt{q}+\mathrm{1个}-ķ$ 来自Baer子平面的点，则结果集具有大小 $q+ķ$ 和 $（\sqrt{q}+\mathrm{1个}-ķ）（q-\sqrt{q}）$0割线。如果我们有更多的0割线，那么我们的主定理说，可以通过从Baer子平面或直线中删除一些点来获得该点集。$\sqrt{q}+\mathrm{1个}-ķ$点并添加一些点。该定理的动机来自平方阶的平面，但是我们的主要结果对于非平方阶也有效。因此，在这种情况下，点集包含相对较大的共线子集。