The unique sum-point conjecture for complete arcs in PG(2,q)PG(2,q)

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Let qq be even, and let a complete arc in the projective plane PG(2,q)PG(2,q) mean an arc that cannot be enlarged by adding another point. Two arcs are projectively equivalent when a projectivity of PG(2,q)PG(2,q) maps one to the other; a sum-point is a point associated with the arc according to the paper's preceding definition. Unique sum-point conjecture. Every complete arc in PG(2,q)PG(2,q) is projectively equivalent to an arc with only one sum-point.

The conjecture proposes a canonical projective representative for every complete arc over an even-order field. Its status is not determined by the supplied text.

References

Primary source

Alexander A. Davydov, Massimo Giulietti, Stefano Marcugini and Fernanda Pambianco, “New inductive constructions of complete caps in PG(N,q), q even”, arXiv:0901.0367 (2009).

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