✦ LIBER ✦

On regular {v, n}-arcs in finite projective spaces

✍ Scribed by Johannes Ueberberg

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 733 KB
Volume: 1
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.3180010603

No coin nor oath required. For personal study only.

✦ Synopsis

A regular {v,n}-arc of a projective space P of order q is a set S of Y points such that each line of P has exactly 0 , l or n points in common with S and such that there exists a line of P intersecting S in exactly n points. Our main results are as follows: (1) If P is a projective plane of order q and if S is a regular {v, n}-arc with n 2 f i + 1, then S is a set of n collinear points, a Baer subplane, a unital, or a maximal arc. (2) If P is a projective space of order q and if S is a regular {v,n}-arc with n 2 f i + 1 spanning a subspace U of dimension at least 3, then S is a Baer subspace of U, an affine space of order q in U, or S equals the point Set Of u.

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