Abstract
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.
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