Related papers: K3-surfaces with special symmetry

In this paper we classify complex K3 surfaces with non-symplectic automorphism of order 8 that leaves invariant a smooth elliptic curve. We show that the rank of the Picard group is either 10, 14 or 18 and the fixed locus is the disjoint…

The present paper provides several results on automorphisms of hyperk\"ahler (or irreducible holomorphic symplectic) manifolds. In particular it focuses on the symplectic case and contains a classification of prime order symplectic…

We classify primitive non-symplectic automorphisms of order 6 on K3 surfaces. We show how their study can be reduced to the study of non-symplectic automorphisms of order 3 and to a local analysis of the fixed loci. In particular, we…

This paper is a survey about $K3$ surfaces with an automorphism and log rational surfaces, in particular, log del Pezzo surfaces and log Enriques surfaces. It is also a reproduction on my talk at "Mathematical structures of integrable…

The present paper proves that finite symplectic groups of automorphisms of hyperk\"ahler fourfolds deformation equivalent to the Hilbert scheme of two points on a $K3$ surface are contained in the simple group $Co_1$. Then we give an…

The present paper is devoted to the classification of symplectic automorphisms of some hyperk\"{a}hler manifolds. The results contained here are an explicit classification of prime order automorphisms on manifolds of $K3^{[n]}$ type and a…

We prove that, for a K3 surface in characteristic p > 2, the automorphism group acts on the nef cone with a rational polyhedral fundamental domain and on the nodal classes with finitely many orbits. As a consequence, for any non-negative…

We investigate the interplay between the moduli spaces of ample <2>-polarized IHS manifolds of type K3^[2] and of IHS manifolds of type K3^[2] with a nonsymplectic involution with invariant lattice of rank one. In particular we…

For $\mathbb Z_3$-orbifold limits of K3, we provide a counterpart to the extensive studies by Nikulin and others of the geometry and symmetries of classical Kummer surfaces. In particular, we determine the group of holomorphic symplectic…

In each characteristic $p\neq 2, 3$, it was shown in a previous work that the order of an automorphism of a K3 surface is bounded by 66, if finite. Here, it is shown that in each characteristic $p\neq 2, 3$ a K3 surface with a cyclic action…

We classify non-symplectic automorphisms of odd prime order on irreducible holomorphic symplectic manifolds which are deformations of Hilbert schemes of any number n of points on K3 surfaces, extending results already known for n=2. In…

Let $k$ be a field of characteristic $0$. In this paper we describe a classification of smooth log K3 surfaces $X$ over $k$ whose geometric Picard group is trivial and which can be compactified into del Pezzo surfaces. We show that such an…

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…

This is an expanded version of our work [AN88], 1988, in Russian. We classify del Pezzo surfaces over C with log terminal singularities of index \le 2. By classification, we understand a description of the intersection graph of all…

We prove that if a K3 surface $X$ admits $\Z/5\Z$ as group of symplectic automorphisms, then it actually admits $\Dh_5$ as group of symplectic automorphisms. The orthogonal complement to the $\Dh_5$-invariants in the second cohomology group…

We show that the Mathieu groups $M_{22}$ and $M_{11}$ can act on the supersingular $K3$ surface with Artin invariant 1 in characteristic 11 as symplectic automorphisms. More generally we show that all maximal subgroups of the Mathieu group…

In this paper, we propose and study a conjecture that symplectic automorphisms of a $K3$ surface $X$ act trivially on the indecomposable part $\mathrm{CH}^2(X,1)_{\mathrm{ind}}\otimes \mathbb{Q}$ of Bloch's higher Chow group. This is a…

For a K3 surface of finite height over a field of odd characteristic, there exists a smooth lifting to the ring of Witt vectors such that the reduction map from the Picard group of the generic fiber to the Picard group of the special fiber…

We present a complete list of extremal elliptic K3 surfaces. There are altogether 325 of them. The first 112 coincides with Miranda-Persson's list for semi-stable ones. The data include the transcendental lattice which determines uniquely…

In this paper we present a classification of non-symplectic automorphisms of K3 surfaces whose order is a multiple of seven by describing the topological type of their fixed locus. In the case of purely non-symplectic automorphisms, we…