Brandhorst and Shimada described a large class of Enriques surfaces, called $(\tau,\overline{\tau})$-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 $10$.

Moschetti, R., Rota, F., Schaffler, L. (2024). The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces. DOCUMENTA MATHEMATICA, 29(5), 1219-1242 [10.4171/dm/972].

The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces

Schaffler, Luca
2024-01-01

Abstract

Brandhorst and Shimada described a large class of Enriques surfaces, called $(\tau,\overline{\tau})$-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 $10$.
2024
Moschetti, R., Rota, F., Schaffler, L. (2024). The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces. DOCUMENTA MATHEMATICA, 29(5), 1219-1242 [10.4171/dm/972].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/485650
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