Algebraic and Arithmetic Geometry Seminar

The non-degeneracy invariant of Enriques surfaces: a computational approach

by Luca Schaffler (Roma)

Aula Seminari (Department of Mathematics)

Aula Seminari

Department of Mathematics

For an Enriques surface S, the non-degeneracy invariant nd(S) retains information about the elliptic fibrations of S and its projective realizations. While this invariant is well understood for general Enriques surfaces, computing it becomes challenging when specializing our Enriques surface. In this talk, we introduce a combinatorial version of the non-degeneracy invariant that depends on S along with a configuration of smooth rational curves, and gives a lower bound for nd(S). We also provide a SageMath code that computes this combinatorial invariant and we apply it in several examples where nd(S) was previously unknown. In particular, we study the families of Enriques surfaces introduced by Brandhorst and Shimada. The results presented are joint works and ongoing projects with Riccardo Moschetti and Franco Rota.