Related papers: Dynamics on supersingular K3 surfaces
We show that K3 surfaces in characteristic 2 can admit sets of $n$ disjoint smooth rational curves whose sum is divisible by 2 in the Picard group, for each $n=8,12,16,20$. More precisely, all values occur on supersingular K3 surfaces, with…
In this paper, we study non-symplectic automorphisms of order 3 on algebraic $K3$ surface over $\mathbb{C}$ which act trivially on the N\'{e}ron-Severi lattice. In particular we shall characterize their fixed locus in terms of the…
We determine the automorphism group of an open log K3 surface with irreducible boundary.
We show how to construct non-isotrivial families of supersingular K3 surfaces over rational curves using a relative form of the Artin-Tate isomorphism and twisted analogues of Bridgeland's results on moduli spaces of stable sheaves on…
Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite…
In this article we give a strategy to decide whether the logarithm of a given Salem number is realized as entropy of an automorphism of a supersingular K3 surface in positive characteristic. As test case it is proved that $\log \lambda_d$,…
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 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…
Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…
We characterize the Artin invariant of a smooth K3 hypersurface in terms of quasi-$F$-splitting. As an application, we obtain an explicit formula for this invariant.
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…
We show that there is a good notion of irreducible sympelectic varieties of $\mathrm{K3}^{[n]}$-type over an arbitrary field of characteristic zero or $p > n + 1$. Then we construct mixed characteristic moduli spaces for these varieties.…
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…
The supersingular K3 surface X in characteristic 2 with Artin invariant 1 admits several genus 1 fibrations (elliptic and quasi-elliptic). We use a bijection between fibrations and definite even lattices of rank 20 and discriminant 4 to…
An automorphism of order $n$ of a K3 surface is called purely non-symplectic if it multiplies the holomorphic symplectic form by a primitive $n$-th root of unity. We give the classification of purely non-symplectic automorphisms with…
We classify elliptic K3 surfaces in characteristic $p$ with $p^n$-torsion sections. For $p^n\geq3$ we verify conjectures of Artin and Shioda, compute the heights of their formal Brauer groups, as well as Artin invariants and Mordell--Weil…
In this paper we investigate when the generic member of a family of K3 surfaces admitting a non--symplectic automorphism of finite order admits also a symplectic automorphism of the same order. We give a complete answer to this question if…
Over an algebraically closed field, various finiteness results are known regarding the automorphism group of a K3 surface and the action of the automorphisms on the Picard lattice. We formulate and prove versions of these results over…
We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of $K3^{[n]}$ type is, in fact, induced by an automorphism of a $K3$ surface and the manifold is a moduli…
We show that every supersingular K3 surface is birational to a double cover of a projective plane.