12 citations · 41 across the 21 of their papers we have counts for
25 papers
Automorphisms and canonical forms of integer lattices
Simon Brandhorst, Tommy Hofmann
We improve the Plesken--Souvignier algorithm for computing automorphism groups and isometries of positive definite integer quadratic lattices by exploiting characteristic sublattic…
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…
On hyperbolic lattices whose reduced automorphism group is virtually abelian
Simon Brandhorst, Markus Kirschmer, Giacomo Mezzedimi
We give a classification of even integral lattices with virtually abelian reduced automorphism group. As a consequence, we complete the classification of K3 surfaces with virtually…
Orbits of smooth rational curves on Enriques surfaces
Simon Brandhorst, Víctor 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…
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…
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…
527 elliptic fibrations on Enriques surfaces
Simon Brandhorst, Víctor González-Alonso
Barth and Peters showed that a general complex Enriques surface has exactly 527 isomorphism classes of elliptic fibrations. We show that every Enriques surface has precisely 527 is…
Elliptic Fibrations on Vinberg's Most Algebraic K3 Surface
Simon Brandhorst, Matthias Zach
We explain how to use the computer algebra system OSCAR to find all elliptic fibrations (up to automorphism) on a given surface and compute their Weierstrass models. This is illust…
Hensel lifting algorithms for quadratic forms
Simon Brandhorst, Davide Cesare Veniani
We provide an algorithm to compute generators of the orthogonal group of the discriminant group associated to an integral quadratic lattice over the integers. We give a closed form…
Borcherds lattices and K3 surfaces of zero entropy
Simon Brandhorst, Giacomo Mezzedimi
Let be an even, hyperbolic lattice with infinitely many simple -roots. We call a Borcherds lattice if it admits an isotropic vector with bounded inner product with al…
Finite subgroups of automorphisms of K3 surfaces
Simon Brandhorst, Tommy Hofmann
We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certai…
Generation of Local Unitary Groups
Simon Brandhorst, Tommy Hofmann, Sven Manthe
Let be a two-dimensional étale algebra over a non-Archimedean local field of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over…
Equations for a K3 Lehmer map
Simon Brandhorst, Noam D. Elkies
McMullen proved that there exists an automorphism of minimal topological entropy on a projective K3 surface. We derive equations for the surface and its automorphism. We reconstruc…
Automorphism groups of certain Enriques surfaces
Simon Brandhorst, Ichiro Shimada
We calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general -nodal Enriques surfaces and very general cuspid…
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…
Prime order isometries of unimodular lattices and automorphisms of ihs manifolds
Simon Brandhorst, Alberto Cattaneo
We characterize conjugacy classes of isometries of odd prime order in unimodular Z-lattices. This is applied to give a complete classification of odd prime order non-symplectic aut…
Extensions of maximal symplectic actions on K3 surfaces
Simon Brandhorst, Kenji Hashimoto
We classify pairs consisting of a complex K3 surface and a finite group such that the subgroup consisting of symplectic automorphisms is a…
On characteristic polynomials of automorphisms of Enriques surfaces
Simon Brandhorst, Sławomir Rams, Ichiro Shimada
Let be an automorphism of a complex Enriques surface and let denote the characteristic polynomial of the isometry of the numerical Néron-Severi lattice of i…
Borcherds' method for Enriques surfaces
Simon Brandhorst, Ichiro Shimada
We classify all primitive embeddings of the lattice of numerical equivalence classes of divisors of an Enriques surface with the intersection form multiplied by 2 into an even unim…
On the stable dynamical spectrum of complex surfaces
Simon Brandhorst
We characterize Salem numbers which have some power arising as dynamical degree of an automorphism on a complex (projective) 2-Torus, K3 or Enriques surface.
Automorphisms of minimal entropy on supersingular K3 surfaces
Simon Brandhorst, Víctor González-Alonso
In this article we give a strategy to decide whether the logarithm of a given Salem number is realized as entropy of an automorphism of a supersingular K3 surface in positive chara…
Automorphisms of Salem degree 22 on supersingular K3 surfaces of higher Artin invariant
Simon Brandhorst
We give a short proof that every supersingular K3 surface (except possibly in characteristic with Artin invariant ) has an automorphism of Salem degree 22. In particular…
The classification of purely non-symplectic automorphisms of high order on K3 surfaces
Simon Brandhorst
An automorphism of order of a K3 surface is called purely non-symplectic if it multiplies the holomorphic symplectic form by a primitive -th root of unity. We give the class…
Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22
Simon Brandhorst
In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic…