In this paper, we generalize the so-called Korchmáros—Mazzocca arcs, that is, point sets of size q + t intersecting each line in 0, 2 or t points in a finite projective plane of order q. For t ≠ 2, this means that each point of the point set is incident with exactly one line meeting the point set in t points.

In PG(2, pⁿ), we change 2 in the definition above to any integer m and describe all examples when m or t is not divisible by p. We also study mod p variants of these objects, give examples and under some conditions we prove the existence of a nucleus.

中文翻译：

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泛化Korchmáros-Mazzocca弧

在本文中，我们概括所谓Korchmáros-Mazzocca弧，即，点集的大小q +吨相交在0,2或每行吨个量级的有限射影平面q。对于t ≠2，这意味着该点集的每个点都与恰好一条线相交，该直线与t点中的点集相交。

在PG（2，p ⁿ）中，我们将以上定义中的2更改为任何整数m，并描述m或t无法被p整除的所有示例。我们还研究了这些物体的mod p变体，给出了例子，并在某些条件下证明了核的存在。