Related papers: On a classical correspondence between K3 surfaces

This paper concerns K3 surfaces with automorphisms of order 11 in arbitrary characteristic. Specifically we study the wild case and prove that a general such surface in characteristic 11 has Picard number 2. We also construct K3 surfaces…

The isometry between the type IV$_6$ and the type II$_4$ hermitian symmetric domains suggests a possible relation between suitable moduli spaces of K3 surfaces of Picard rank $14$ and of polarised abelian $8$-folds with totally definite…

We show that the moduli space of ordered 5 points on the projective line is isomorphic to an arithmetic quotient of a complex ball by using the theory of periods of K3 surfaces. We also discuss a relation between our uniformization and the…

We consider a semistable degeneration of K3 surfaces, equipped with an effective divisor that defines a polarisation of degree two on a general fibre. We show that the map to the relative log canonical model of the degeneration maps every…

We have the correspondences between Lucas sequences, Pell's equations, and the automorphisms of K3 surfaces with Picard number 2. Using these correspondences, we determine the intersections of some Lucas sequences.

An element in the Brauer group of a general complex projective $K3$ surface $S$ defines a sublattice of the transcendental lattice of $S$. We consider those elements of prime order for which this sublattice is Hodge-isometric to the…

Let us consider the rank 14 lattice $P=D_4^3\oplus < -2> \oplus < 2>$. We define a K3 surface S of type P with the property that $P\subset {\rm Pic}(S) $, where ${\rm Pic}(S) $ indicates the Picard lattice of S. In this article we study 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 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…

This paper studies curves on quartic K3 surfaces, or more generally K3 surfaces which are complete intersection in weighted projective spaces. A folklore conjecture concerning rational curves on K3 surfaces states that all K3 surfaces…

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…

In a previous paper, math.AG/0409419, we described six families of K3-surfaces with Picard-number 19, and we identified surfaces with Picard-number 20. In these notes we classify some of the surfaces by computing their transcendental…

In this paper we show that the moduli space of nodal cubic surfaces is isomorphic to a quotient of a 4-dimensional complex ball by an arithmetic subgroup of the unitary group. This complex ball uniformization uses the periods of certain K3…

We first prove an isomorphism between the moduli space of smooth cubic threefolds and the moduli space of hyperkaehler fourfolds of K3^{[2]}-type with a non-symplectic automorphism of order three, whose invariant lattice has rank one and is…

We study generalized complex structures on K3 surfaces, in the sense of Hitchin. For each real parameter t between one and infinity we exhibit two families of generalized K3 surfaces, (M,cal{I}_{zeta}) and (M,cal{J}_{zeta}), parametrized by…

Nikulin and Vinberg proved that there are only a finite number of lattices of rank $\geq 3$ that are the N\'eron-Severi group of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric…

We determine explicit birational models over Q for the modular surfaces parametrising pairs of N-congruent elliptic curves in all cases where this surface is an elliptic surface. In each case we also determine the rank of the Mordell-Weil…

We take a first step towards the classification of singular Mori dream $K3$ surfaces. We prove that if the Picard lattice of a singular $K3$ surface is Mori dream, then the surface is Mori dream. Moreover, we show that for singular $K3$…

Let $X$ be a K3 surface with Picard group $\mathrm{Pic}(X)\cong\mathbb{Z} H$ such that $H^2=2n$. Let $M_{H}(\mathbf{v})$ be the moduli space of Gieseker semistable sheaves on $X$ with Mukai vector $\mathbf{v}$. We say that $\mathbf{v}$…

We exhibit explicit examples of very general special cubic fourfolds with discriminant $d$ admitting an associated (twisted) K3 surface, which have non-isomorphic Fourier-Mukai partners. In particular, in the untwisted setting, we show that…