Unitals of PG(2,q^2) containing conics

Details Unitals of PG(2,q^2) containing conics Unitals of PG(2,q^2) containing conics

2012-03-08

arxiv.org/abs/1203.1766v1

Mathematics

Combinatorics

Scientific paper

A unital in PG(2,q^2) is a set U of q^3+1 points such that each line meets U in 1 or q+1 points. The well known example is the classical unital consisting of all absolute points of a non-degenerate unitary polarity of PG(2,q^2). Unitals other than the classical one also exist in PG(2,q^2) for every q>2. Actually, all known unitals are of Buekenhout-Metz type and they can be obtained by a construction due to Buekenhout. The unitals constructed by Baker-Ebert, and independently by Hirschfeld-Szonyi, are the union of q conics. Our Theorem 1.1 shows that this geometric property characterizes the Baker-Ebert-Hirschfeld-Szonyi unitals.

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