We construct highly symmetric arcs by using highly symmetric curves: the Klein quartic which is the most symmetric non-singular curve of degree 4, and the Wiman sextic which is shown to be the unique A(6)-invariant curve of degree 6. The set of flexes of the Klein quartic is a 24-arc with automorphism group PSL(2,7), while the set of flexes of the Wiman sextic is a 72-are with automorphism group PSL(2,9) similar or equal to A(6).
On arcs and curves with many automorphisms
MARCUGINI, Stefano;PAMBIANCO, Fernanda
2005
Abstract
We construct highly symmetric arcs by using highly symmetric curves: the Klein quartic which is the most symmetric non-singular curve of degree 4, and the Wiman sextic which is shown to be the unique A(6)-invariant curve of degree 6. The set of flexes of the Klein quartic is a 24-arc with automorphism group PSL(2,7), while the set of flexes of the Wiman sextic is a 72-are with automorphism group PSL(2,9) similar or equal to A(6).File in questo prodotto:
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