Related papers: Finiteness theorems for K3 surfaces over arbitrary…

We study the maximal Salem degree of automorphisms of K3 surfaces via elliptic fibrations. By generalizing \cite{EOY14}, we establish a characterization of such maximum in terms of elliptic fibrations with infinite automorphism groups. As…

The aim of this paper is to generalize results known for the symplectic involutions on K3 surfaces to the order 3 symplectic automorphisms on K3 surfaces. In particular, we will explicitly describe the action induced on the lattice…

In this paper we study K3 surfaces with a non-symplectic automorphism of order 3. In particular, we classify the topological structure of the fixed locus of such automorphisms and we show that it determines the action on cohomology. This…

We classify possible finite groups of symplectic automorphisms of K3 surfaces of order divisible by 11. The characteristic of the ground field must be equal to 11. The complete list of such groups consists of five groups: the cyclic group…

This is a brief introduction to the theory of Enriques surfaces over arbitrary algebraically closed fields. Some new results about automorphism groups of Enriques surfaces are also included.

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 reconstruct the surface and its automorphism from the Hodge theoretic…

We show that every finite group occurs as the automorphism group of infinitely many finite (field) extensions of any given Hilbertian field. This extends and unifies previous results of M. Fried and Takahashi on the global field case.

We introduce the notion of the $k$-closure of a group of automorphisms of a locally finite tree, and give several examples of the construction. We show that the $k$-closure satisfies a new property of automorphism groups of trees that…

We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell-Weil group on K3 surfaces with infinite automorphism group and 2-elementary…

Given a K3 surface X over a field of characteristic p, Artin conjectured that if X is supersingular (meaning infinite height) then its Picard rank is 22. Along with work of Nygaard-Ogus, this conjecture implies the Tate conjecture for K3…

We calculate the automorphism group of the Kummer surface associated with a curve of genus 2 or the product of two elliptic curves in characteristic two under the assumption that the Kummer surface is a $K3$ surface. Moreover we discuss the…

If an automorphism of a projective K3 surface with Picard number 2 is of infinite order, then the automorphism corresponds to a solution of Pell equation. In this paper, by solving this equation, we determine all Salem polynomials of…

In this paper, we prove that, over an algebraically closed field whose characteristic is not 2,3 nor 7, a pair of a K3 surface and a purely non-symplectic automorphism of order 21 or 42 is unique up to isomorphism.

We shall characterize the Fermat K3 surface, among all complex K3 surfaces, by means of its finite group symmetries.

We study orbit closures and stationary measures for groups of automorphisms of $p$-adic affine surfaces.

Let $X$ be a K3 surface defined over a number field $K$. Assume that $X$ admits a structure of an elliptic fibration or an infinite group of automorphisms. Then there exists a finite extension $K'/K$ such that the set of $K'$-rational…

We show that if $K$ is an arbitrary field and $G$ is a finite group then there exists a curve over $K$ with automorphism group $G$. We also give a positive solution to the weak inverse Galois problem for function fields over an arbitrary…

We give an alternative proof of a result of Cantat and Dupont, showing that any automorphism of a K3 surface with measure of maximal entropy in the Lebesgue class must be a Kummer example. Our method exploits the existence of Ricci-flat…

These notes will give an introduction to the theory of K3 surfaces. We begin with some general results on K3 surfaces, including the construction of their moduli space and some of its properties. We then move on to focus on the theory of…

We review recent developments in the arithmetic of K3 surfaces. Our focus lies on aspects of modularity, Picard number and rational points. Throughout we emphasise connections to geometry.