Geodesic
The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces
Documenta mathematica, Tome 29 (2024) no. 5, pp. 1219-1242

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Brandhorst and Shimada described a large class of Enriques surfaces, called (τ,τˉ)-generic, for which they gave generators for the automorphism groups and calculated the elliptic fibrations and the smooth rational curves up to automorphisms. In the present paper, we give lower bounds for the non-degeneracy invariant of such Enriques surfaces, we show that in most cases the invariant has generic value 10, and we present the first known example of complex Enriques surface with infinite automorphism group and non-degeneracy invariant not equal to 10.
DOI : 10.4171/dm/972
Classification : 14J28, 14J50, 14Q10
Mots-clés : Enriques surface, elliptic fibration, rational curve, automorphism, non-degeneracy invariant 
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Riccardo Moschetti; Franco Rota; Luca Schaffler. The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces. Documenta mathematica, Tome 29 (2024) no. 5, pp. 1219-1242. doi: 10.4171/dm/972

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