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- W2963608183 abstract "A k-arc in the projective space $$mathrm{PG}(n,q)$$ is a set of k projective points such that no subcollection of $$n+1$$ points is contained in a hyperplane. In this paper, we construct new 60-arcs and 110-arcs in $$mathrm{PG}(4,q)$$ that do not arise from rational or elliptic curves. We introduce computational methods that, when given a set $$mathcal {P}$$ of projective points in the projective space of dimension n over an algebraic number field $${mathbb {Q}}(xi )$$ , determines a complete list of primes p for which the reduction modulo p of $$mathcal {P}$$ to the projective space $$mathrm{PG}(n,p^h)$$ may fail to be a k-arc. Using these methods, we prove that there are infinitely many primes p such that $$mathrm{PG}(4,p)$$ contains a $$mathrm{PSL}(2,11)$$ -invariant 110-arc, where $$mathrm{PSL}(2,11)$$ is given in one of its natural irreducible representations as a subgroup of $$mathrm{PGL}(5,p)$$ . Similarly, we show that there exist $$mathrm{PSL}(2,11)$$ -invariant 110-arcs in $$mathrm{PG}(4,p^2)$$ and $$mathrm{PSL}(2,11)$$ -invariant 60-arcs in $$mathrm{PG}(4,p)$$ for infinitely many primes p." @default.
- W2963608183 created "2019-07-30" @default.
- W2963608183 creator A5048432131 @default.
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- W2963608183 date "2018-11-29" @default.
- W2963608183 modified "2023-09-25" @default.
- W2963608183 title "Transitive PSL(2,11)-invariant k-arcs in PG(4,q)" @default.
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- W2963608183 doi "https://doi.org/10.1007/s10623-018-0588-9" @default.
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