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 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.
Unitals of PG(2, q^2 ) containing conics
SICILIANO, Alessandro
2013-01-01
Abstract
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 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.File in questo prodotto:
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