6 papers
Automorphisms of Nikulin-type orbifolds
Simon Brandhorst, Grégoire Menet, Stevell Muller
Nikulin-type orbifolds are certain singular 4-dimensional irreducible holomorphic symplectic varieties. We show that the monodromy group of Nikulin-type orbifolds is maximal and cl…
The Cone Conjecture for Enriques Surfaces in any Characteristic
Simon Brandhorst, Gebhard Martin, Tobias Schnieders
We give a proof of the Morrison-Kawamata cone conjecture for Enriques surfaces independent of their characteristic. It is based on the analysis of certain generically finite morphi…
Virtually abelian symmetry groups of hyperbolic lattices
Simon Brandhorst, Markus Kirschmer, Giacomo Mezzedimi
We give a classification of integral lattices with virtually abelian symmetry group. As a consequence, we complete the classification of K3 surfaces with virtually abelian automorp…
Orbits of smooth rational curves on Enriques surfaces
Simon Brandhorst, VÃctor González-Alonso
We give a closed formula for the number of orbits of smooth rational curves under the automorphism group of an Enriques surface in terms of its Nikulin root invariant and its Vinbe…
Idoneal genera and K3 surfaces covering an Enriques surface
Simon Brandhorst, Serkan Sonel, Davide Cesare Veniani
Idoneal genera are a generalization of Euler's idoneal numbers. We enumerate all idoneal genera by means of the Smith--Minkowski--Siegel mass formula. As an application, we classif…
An explicit Enriques surface with an automorphism of minimum entropy
Simon Brandhorst, Matthias Zach
We derive explicit equations for the Oguiso-Yu automorphism of minimum topological entropy on a complex Enriques surface. The approach is computer aided and makes use of elliptic f…