Abstract
The operator \(\Lambda _{\{2\},\{3\}}\) acting on line arrangements is defined by associating to a line arrangement 
, the line arrangement which is the union of the lines containing exactly three points among the double points of 
. We say that six lines not tangent to a conic form an unassuming arrangement if the singularities of their union are only double points, but the dual line arrangement has six triple points, six 5-points and 27 double points. The moduli space of unassuming arrangements is the union of a point and a line. The image by the operator \(\Lambda _{\{2\},\{3\}}\) of an unassuming arrangement is again an unassuming arrangement. We study the dynamics of the operator \(\Lambda _{\{2\},\{3\}}\) on these arrangements and we obtain that the periodic arrangements are related to the Ceva arrangements of lines.
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Acknowledgements
The author is grateful to Lukas Kühne for his explanations on the realization of matroids and pointing out the paper [1]; he is also grateful to the referees for their comments improving the paper.
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Roulleau, X. On the dynamics of the line operator \(\Lambda _{\{2\},\{3\}}\) on some arrangements of six lines. European Journal of Mathematics 9, 105 (2023). https://doi.org/10.1007/s40879-023-00699-w
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DOI: https://doi.org/10.1007/s40879-023-00699-w