Related papers: Order 3 symplectic automorphisms on K3 surfaces

In this paper we consider the class of K3 surfaces defined as hypersurfaces in weighted projective space, and admitting a non-symplectic automorphism of non-prime order, excluding the orders 4, 8, and 12. We show that on these surfaces the…

In this paper, we consider the problem of determining which automorphisms of a smooth quartic surface $S \subset \mathbb{P}^3$ are induced by a Cremona transformation of $\mathbb{P}^3$. We provide the first steps towards a complete solution…

We give a systematic method to calculate some homological data from the global monodromy of a topological elliptic surface. We apply this method to the cases 1) the transcendental lattice of an extremal elliptic K3 surface, 2) the torsion…

In this paper, we prove that, over an algebraically closed field of odd characteristic, a weakly tame automorphism of a K3 surface of finite height can be lifted over the ring of Witt vectors of the base field. Also we prove that a…

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…

If an automorphism of a projective K3 surface with Picard number 2 is of infinite order, then the automorphism corresponds to a solution of Pell equation. In this paper, by solving this equation, we determine all Salem polynomials of…

We compute entropies in a large family of K3 surface automorphisms in (P^1)^3. In keeping with a result by Xie, we find that the entropies vary in a lower semi-continuous manner as the Picard ranks of the K3 surfaces vary.

The Shafarevich conjecture for K3 surfaces asserts the finiteness of isomorphism classes of K3 surfaces over a fixed number field admitting good reduction away from a fixed finite set of finite places. Andr\'{e} proved this conjecture for…

A few facts concerning the phrase "the automorphism groups become larger at special points of the moduli of K3 surfaces" are presented. It is also shown that the automorphism groups are of infinite order over a dense subset in any…

Let $X$ be a K3 or Enriques surface with good reduction. Let $G$ be a finite group acting (not necessarily linearly) on $X$. We give a criterion for this group action to extend to a smooth model of $X$ in terms of the action of $G$ on the…

In this work we classify all smooth surfaces with geometric genus equal to three and an action of a group G isomorphic to (Z/2)^k such that the quotient is a plane. We find 11 families. We compute the canonical map of all of them, finding…

We study generalized Kummer surfaces Km$_{3}(A)$, by which we mean the K3 surfaces obtained by desingularization of the quotient of an abelian surface $A$ by an order $3$ symplectic automorphism group. Such a surface carries $9$ disjoint…

From the viewpoint of mirror symmetry, we revisit the hypergeometric system $E(3,6)$ for a family of K3 surfaces. We construct a good resolution of the Baily-Borel-Satake compactification of its parameter space, which admits special…

We prove gap theorems for entropy norms on automorphism groups of K3 surfaces, Enriques surfaces, and irreducible holomorphic symplectic manifolds. We also study the achirality of automorphisms of K3 surfaces and Enriques surfaces in terms…

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 construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under…

The aim of this note is to characterize a K3 surface of Klein-Mukai type in terms of its symmetry.

Every Salem numbers of degree 4,6,8,12,14 or 16 is the dynamical degree of an automorphism of a non-projective K3 surface. We define a notion of signature of an automorphism, and use it to give a necessary and sufficient condition for Salem…

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…

We realize the logarithm of the third smallest known Salem number as the topological entropy of a K3 surface automorphism with a Siegel disk and a pointwisely fixed curve at the same time. We also show the logarithm of the Lehmer number,…