Related papers: Order 9 automorphisms of K3 surfaces

We give a necessary and sufficient condition for an automorphism of the Hilbert scheme of points on a K3 surface (non necessarily algebraic) to be induced by an automorphism of the surface. We prove furthermore that the group of birational…

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…

The moduli space of K3 surfaces $X$ with a purely non-symplectic automorphism $\sigma$ of order $n\geq 2$ is one dimensional exactly when $\varphi(n)=8$ or $10$. In this paper we classify and give explicit equations for the very general…

We study K3 surfaces with a pair of commuting involutions that are non-symplectic with respect to two anti-commuting complex structures that are determined by a hyper-K\"ahler metric. One motivation for this paper is the role of such…

We show that K3 surfaces with non-symplectic automorphisms of prime order can be used to construct new compact irreducible G2-manifolds. This technique was carried out in detail by Kovalev and Lee for non-symplectic involutions. We use…

In this paper we study the automorphisms group of some $K3$ surfaces which are double covers of the projective plane ramified over a smooth sextic plane curve. More precisely, we study the case of a $K3$ surface of Picard rank two such that…

Smooth and symplectic symmetries of an infinite family of distinct exotic $K3$ surfaces are studied, and comparison with the corresponding symmetries of the standard $K3$ is made. The action on the $K3$ lattice induced by a smooth finite…

Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we…

In this note, we report some progress we made recently on the automorphisms groups of K3 surfaces. A short and straightforward proof of the impossibility of Z/(60) acting purely non-symplectically on a K3 surface, is also given, by using…

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…

We prove the main Conjecture 4 of our paper arXiv:1403.6061v5, which leads to classification of degenerations of codimension one of Kahlerian K3 surfaces with finite symplectic automorphism groups.

The aim of this paper is to give necessary and sufficient conditions for an integral polynomial to be the characteristic polynomial of a semi-simple isometry of some even unimodular lattice of given signature. This result has applications…

Let k=F_q be a finite field of even characteristic. We obtain in this paper a complete classification, up to k-isomorphism, of non singular quartic plane curves defined over k. We find explicit rational normal models and we give closed…

We classify, up to automorphisms, the elliptic fibrations on the singular K3 surface $X$ whose transcendental lattice is isometric to $\langle 6\rangle\oplus \langle 2\rangle$.

We classify prime order isogenies between algebraic K3 surfaces whose rational transcendental Hodges structures are not isometric. The morphisms of Hodge structures induced by these isogenies are correspondences by algebraic classes on the…

Given $X$ a K3 surface admitting a symplectic automorphism $\tau$ of order 4, we describe the isometry $\tau^*$ on $H^2(X,\mathbb Z)$. Having called $\tilde Z$ and $\tilde Y$ respectively the minimal resolutions of the quotient surfaces…

We prove that a K3 surface with an automorphism acting on the global $2$-forms by a primitive $m$-th root of unity, $m \neq 1,2,3,4,6$, does not degenerate (assuming the existence of the so-called Kulikov models). A key result used to prove…

We study non-symplectic involutions on irreducible symplectic manifolds of K3^{[2]}-type with 19 parameters, which is the second largest possible. We classify the conjugacy classes of cohomological representations into four different types…

In characteristic $0$, symplectic automorphisms of K3 surfaces (i.e.\ automorphisms preserving the global $2$-form) and non-symplectic ones behave differently. In this paper we consider the actions of the group schemes $\mu_{n}$ on K3…

We classify Coble surfaces with finite automorphism group in arbitrary characteristic not equal to 2. There are exactly 9 isomorphism classes of such surfaces.