Extending the construction to even values of n

Construct, for even values of n, a dihedral or more general finite-group action whose de Jonquières iteration remains nondegenerate and produces an analogous irrational limiting nef ray.

Background

The main construction applies to odd integers n at least 5. It uses specific dihedral weights and an alternating sequence of de Jonquières transformations; the resulting iteration is proved to remain nondegenerate and to converge projectively to an irrational nef isotropic ray.

The authors leave unresolved whether an analogous construction exists for even n. The proposed direction is to replace the chosen weights by another dihedral action, or by a more general finite-group action, while preserving nondegeneracy of the de Jonquières iteration and obtaining an irrational limiting ray suitable for producing irrational Seshadri constants.

References

For even values of $n$, can one replace the present choice of weights by a different dihedral or more general finite-group action so that the de Jonquières iteration remains nondegenerate and produces an analogous irrational limiting ray?

— Dihedral reflections and an infinite series of irrational Seshadri constants  (2610.01783 - Malara et al., 1 Oct 2026) in Section “Further remarks and possible extensions,” Question environment