Related papers: K3 Surfaces with Involution and Analytic Torsion

We study families of $K3$ surfaces obtained by double covering of the projective plane branching along curves of $(2,3)$-torus type. In the first part, we study the Picard lattices of the families, and a lattice duality of them. In the…

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 extend our recent study of K3 metrics near the $T^4/Z_2$ orbifold locus to the other torus orbifold loci. In particular, we provide several new constructions of K3 surfaces as hyper-K\"ahler quotients, which yield new formulae for K3…

We calculate the automorphism group of the Kummer surface associated with a curve of genus 2 or the product of two elliptic curves in characteristic two under the assumption that the Kummer surface is a $K3$ surface. Moreover we discuss the…

In this paper, combining Kirillov's method of orbits with Connes' method in Differential Geometry, we study the so-called MD(5,3C)-foliations, i.e. the orbit foliations of the co-adjoint action of MD(5,3C)-groups. First, we classify…

In this paper we study equivariant moduli spaces of sheaves on a $ K3 $ surface $ X $ under a symplectic action of a finite group. We prove that under some mild conditions, equivariant moduli spaces of sheaves on $ X $ are irreducible…

We classify all Jacobian elliptic fibrations on K3 surfaces with finite automorphism group. We also classify all Jacobian elliptic fibrations with finite Mordell-Weil group on K3 surfaces with infinite automorphism group and 2-elementary…

Given a K3 surface X over a field of characteristic p, Artin conjectured that if X is supersingular (meaning infinite height) then its Picard rank is 22. Along with work of Nygaard-Ogus, this conjecture implies the Tate conjecture for K3…

We construct K3 surfaces over number fields that have good reduction everywhere. These do not exists over the rational numbers, by results of Abrashkin and Fontaine. Our surfaces exist for three quadratic number fields, and an infinite…

We give variants of lifting construction, which define new classes of modular forms on the Siegel upper half-space of complex dimension 3 with respect to the full paramodular groups (defining moduli of Abelian surfaces with arbitrary…

In this paper we complete the classification of the elliptic fibrations on K3 surfaces which admit a non-symplectic involution acting trivially on the N\'eron--Severi group. We use the geometric method introduced by Oguiso and moreover we…

We study isogenies between K3 surfaces in positive characteristic. Our main result is a characterization of K3 surfaces isogenous to a given K3 surface $X$ in terms of certain integral sublattices of the second rational $\ell$-adic and…

In this paper we show that there is a correspondence between some $K3$ surfaces with non-isometric transcendental lattices constructed as a twist of the transcendental lattice of the Jacobian of a generic genus 2 curve. Moreover, we show…

This article primarily aims at classifying, on certain K3 surfaces, the elliptic fibrations induced by conic bundles on smooth del Pezzo surfaces. The key geometric tool employed is the Alexeev-Nikulin correspondence between del Pezzo…

Let X be a holomorphic symplectic manifold, of dimension divisible by 4, and s an antisymplectic involution of X . The fixed locus F of s is a Lagrangian submanifold of X ; we show that its \^A-genus is 1. As an application, we determine…

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…

The combinatorial type of an elliptic K3 surface with a zero section is the pair of the ADE -type of singular fibers and the torsion part of the Mordell-Weil group. We determine the set of connected components of the moduli of elliptic K3…

We consider a moduli space of lattice polarized K3 surfaces with the additional information of a frame of the trascendental cohomology with respect to the lattice polarization. This moduli space is proved to be quasi-affine, and the…

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 some particlar case of a K3 surface of Picard rank two.

We determine explicit generators for the ring of modular forms associated with the moduli spaces of K3 surfaces with automorphism group $(\mathbb{Z}/2\mathbb{Z})^2$ and of Picard rank 13 and higher. The K3 surfaces in question carry a…