2-semiarcs in PG(2, q), q ≤ 13

Bartoli, D and Faina, G and Kiss, György and Marcugini, S and Pambianco, F (2014) 2-semiarcs in PG(2, q), q ≤ 13. ARS COMBINATORIA, 117. pp. 435-462. ISSN 0381-7032

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Abstract

A 2-semiarc is a pointset S2 with the property that the number of tangent lines to S2 at each of its points is two. Using some theoretical results and computer aided search, the complete classification of 2-semiarcs in PG(2, q) is given for q ≤ 7, the spectrum of their sizes is determined for q ≤ 9, and some results about the existence are proven for q = 11 and q = 13. For several sizes of 2-semiarcs in PG(2, q), q ≤ 7, classification results have been obtained by theoretical proofs.

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