Related papers: On K3 surface quotients of K3 or Abelian surfaces

Let $G$ be a finite abelian group which acts symplectically on a K3 surface. The N\'eron-Severi lattice of the projective K3 surfaces admitting $G$ symplectic action and with minimal Picard number is computed by Garbagnati and Sarti. We…

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…

The quotient space of a $K3$ surface by a finite group is an Enriques surface or a rational surface if it is smooth. Finite groups where the quotient space are Enriques surfaces are known. In this paper, by analyzing effective divisors on…

Let $\Bbbk$ be any field of characteristic zero, $X$ be a cubic surface in $\mathbb{P}^3_{\Bbbk}$ and $G$ be a group acting on $X$. We show that if $X(\Bbbk) \ne \varnothing$ and $G$ is not trivial and not a group of order $3$ acting in a…

We consider the symplectic action of a finite group G on a K3 surface. The Picard group of the K3 surface has a primitive sublattice determined by G. We show how to compute the rank and discriminant of this sublattice. We then describe…

We classify all the K3 surfaces which are minimal models of the quotient of the product of two curves $C_1\times C_2$ by the diagonal action of either the group $\Z/p\Z$ or the group $\Z/2p\Z$. These K3 surfaces admit a non-symplectic…

We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits…

We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W. Barth and the second author. We give here an easy proof that…

We study finite abelian groups acting on three-dimensional rationally connected varieties. We concentrate on the groups of K3 type, that is, abelian extensions by a cyclic group of groups that faithfully act on a K3 surface. In particular,…

We construct various modular compactifications of the space of elliptic K3 surfaces using tools from the minimal model program, and explicitly describe the surfaces parametrized by their boundaries. The coarse spaces of our constructed…

Nikulin and Vinberg proved that there are only a finite number of lattices of rank $\geq 3$ that are the N\'eron-Severi group of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric…

In this paper we continue the study of algebraic fundamentale group of minimal surfaces of general type S satisfying K_S^2<3\chi(S). We show that, if K_S^2= 3\chi(S)-1 and the algebraic fundamental group of S has order 8, then S is a…

Let X be a K3 surface with an involution g which has non-empty fixed locus X^g and acts non-trivially on a non-zero holomorphic 2-form. We shall construct all such pairs (X, g) in a canonical way, from some better known double coverings of…

Let $X/ \mathbb{C}$ be a K3 surface with complex multiplication by the ring of integers of a CM field $E$. We show that $X$ can always be defined over an Abelian extension $K/E$ explicitly determined by the discriminant form of the lattice…

The aim of this paper is to describe algebraic K3 surfaces with an even set of rational curves or of nodes. Their minimal possible Picard number is nine. We completely classify these K3 surfaces and after a carefull analysis of the divisors…

Nikulin has classified all finite abelian groups acting symplectically on a K3 surface and he has shown that the induced action on the K3 lattice $U^3\oplus E_8(-1)^2$ depends only on the group but not on the K3 surface. For all the groups…

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…

Let $X$ be a complex algebraic K3 surface of degree $2d$ and with Picard number $\rho$. Assume that $X$ admits two commuting involutions: one holomorphic and one anti-holomorphic. In that case, $\rho \geq 1$ when $d=1$ and $\rho \geq 2$…

We study Glois embeddings of K3 surfaces in the case where the Galois groups are abelian. We show several properties of K3 surfaces concerning the Galois embeddings. In particular, if the Galois group G is abelian, then G is isomorphic to…

The naive analogue of the N\'eron-Ogg-Shafarevich criterion is false for K3 surfaces, that is, there exist K3 surfaces over Henselian, discretely valued fields $K$, with unramified $\ell$-adic \'etale cohomology groups, but which do not…