The number of automorphism orbits of smooth rational curves on an Enriques surface equals a weighted sum of orbit counts of the ADE components of its Nikulin root invariant under the Vinberg group.
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Orbits of smooth rational curves on Enriques surfaces
The number of automorphism orbits of smooth rational curves on an Enriques surface equals a weighted sum of orbit counts of the ADE components of its Nikulin root invariant under the Vinberg group.