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

  • Riccardo Moschetti

    University of Turin, Torino, Italy
  • Franco Rota

    University of Glasgow, Glasgow, UK
  • Luca Schaffler

    Università degli Studi Roma Tre, Roma, Italy
The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces cover
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Abstract

Brandhorst and Shimada described a large class of Enriques surfaces, called -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 , and we present the first known example of complex Enriques surface with infinite automorphism group and non-degeneracy invariant not equal to .

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Riccardo Moschetti, Franco Rota, Luca Schaffler, The non-degeneracy invariant of Brandhorst and Shimada’s families of Enriques surfaces. Doc. Math. 29 (2024), no. 5, pp. 1219–1242

DOI 10.4171/DM/972