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.
On automorphisms and the cone conjecture for Enriques surfaces in odd characteristic
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abstract
We prove that, for an Enriques surface in odd characteristic, the automorphism group is finitely generated and it acts on the effective nef cone with a rational polyhedral fundamental domain. We also construct a smooth projective surface in odd characteristic which is birational to an Enriques surface and whose automorphism group is discrete but not finitely generated.
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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.