Related papers: Finiteness theorems for K3 surfaces over arbitrary…

For every field $k$ of characteristic zero, we determine the groups that act as automorphisms on a smooth cubic surface over $k$. We also determine the groups that act on $k$-rational, stably $k$-rational, or $k$-unirational smooth cubic…

We present a finite set of generators of the automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3.

We analyze K3 surfaces admitting an elliptic fibration $E$ and a finite group $G$ of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration $E/G$ comparing its properties to the ones of…

We survey recent results on multiple transitivity of automorphism groups of affine algebraic varieties. We consider the property of infinite transitivity of the special automorphism group, which is equivalent to flexibility of the…

This paper gives upper and lower bounds for the degree of the field of definition of a singular K3 surface, generalising a recent result by Shimada. We use work of Shioda-Mitani and Shioda-Inose and classical theory of complex…

We classify Enriques involutions on a K3 surface, up to conjugation in the automorphism group, in terms of lattice theory. We enumerate such involutions on singular K3 surfaces with transcendental lattice of discriminant smaller than or…

The geometric objects of study in this paper are K3 surfaces which admit a polarization by the unique even unimodular lattice of signature (1,17). A standard Hodge-theoretic observation about this special class of K3 surfaces is that their…

We give a classification of maximal elements of the set of finite groups that can be realized as the full automorphism groups of polarized abelian surfaces over finite fields.

Let $k$ be either a number a field or a function field over $\mathbb{Q}$ with finitely many variables. We present a practical algorithm to compute the geometric Picard lattice of a K3 surface over $k$ of degree $2$, i.e., a double cover of…

Given a finite residue field $k$, one looks for a smoothness basis that is invariant under the automorphism group of $k$. We construct models for some finite fields that admit such a basis. This work aims at accelerating algorithms for…

In this paper we describe graded automorphisms and antiautomorphisms of finite order on matrix algebras endowed with a group gradings by a finite abelian group over an arbitrary algebraically closed field of charcteristic different from 2.

Surface groups are determined among limit groups by their profinite completions. As a corollary, the set of surface words in a free group is closed in the profinite topology.

We give an overview of some recent interactions between the geometry of K3 surfaces and their Ricci-flat Kahler metrics and the dynamical study of K3 automorphisms with positive entropy.

We determine the automorphism group of the Hilbert scheme of two points on a generic projective K3 surface of any polarization. We obtain in particular new examples of Hilbert schemes of points having non-natural non-symplectic…

Let $X\subset \P^5$ be a smooth cubic fourfold. A well known conjecture asserts that $X$ is rational if and only if there an Hodge theoretically associated K3 surface $S$. The surface $S$ can be associated to $X$ in two other different…

We have the correspondences between Lucas sequences, Pell's equations, and the automorphisms of K3 surfaces with Picard number 2. Using these correspondences, we determine the intersections of some Lucas sequences.

Let $K$ be a differential field over $\C$ with derivation $D$, $G$ a finite linear automorphism group over $K$ which preserves $D$, and $K^G$ the fixed point subfield of $K$ under the action of $G$. We show that every finite-dimensional…

We treat non-symplectic automorphisms on $K3$ surfaces which act trivially on the N\'{e}ron-Severi lattice. In this paper, we classify non-symplectic automorphisms of prime-power order, especially 2-power order on $K3$ surfaces, i.e., we…

We prove that for any of a wide class of elliptic surfaces $X$ defined over a number field $k$, if there is an algebraic point on $X$ that lies on only finitely many rational curves, then there is an algebraic point on $X$ that lies on no…

Recently S. Patrikis, J.F. Voloch and Y. Zarhin have proven, assuming several well known conjectures, that the finite descent obstruction holds on the moduli space of principally polarised abelian varieties. We show an analogous result for…