Related papers: K3 surfaces with interesting groups of automorphis…

We prove the unpolarized Shafarevich conjecture for K3 surfaces: the set of isomorphism classes of K3 surfaces over a fixed number field with good reduction away from a fixed and finite set of places is finite. Our proof is based on the…

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…

In view of a potential interpretation of the role of the Mathieu group M_24 in the context of strings compactified on K3 surfaces, we develop techniques to combine groups of symmetries from different K3 surfaces to larger 'overarching'…

Recently Oguiso showed the existence of K3 surfaces that admit a fixed point free automorphism of positive entropy. The K3 surfaces used by Oguiso have a particular rank two Picard lattice. We show, using results of Beauville, that these…

We survey some recent progress in the study of algebraic varieties X with log terminal singularities, especially, the uni-ruledness of the smooth locus X^0 of X, the fundamental group of X^0 and the automorphisms group on (smooth or…

We analyze K3 surfaces admitting an elliptic fibration $E$ and a finite group $G$ of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration $E/G$ comparing its properties to the ones of…

In this paper, we study finite symplectic actions on K3 surfaces X, i.e. actions of finite groups G on X which act on H^{2,0}(X) trivially. We show that the action on the K3 lattice H^2(X,Z) induced by a symplectic action of G on X depends…

In this paper, we investigate Bloch's conjecture for autoequivalence on K3 surfaces. We introduce the notion of reflective autoequivalence of twisted K3 surfaces and prove Bloch's conjecture for such autoequivalences, thereby confirming the…

Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for…

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.

Let $L$ be an even, hyperbolic lattice with infinitely many simple $(-2)$-roots. We call $L$ a Borcherds lattice if it admits an isotropic vector with bounded inner product with all the simple $(-2)$-roots. We show that this is the case if…

Nikulin proved that the isometries induced on the second cohomology group of a K3 surface $X$ by a finite abelian group $G$ of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of…

The aim of this paper is to give an explicit description of the fixed loci of symplectic automorphisms for certain hyperkahler manifolds, namely for Hilbert schemes on K3 surfaces and for generalized Kummer varieties. Here we extend our…

Using the general method which was applied to prove finiteness of the set of hyperbolic generalized Cartan matrices of elliptic and parabolic type, we classify all symmetric (and twisted to symmetric) hyperbolic generalized Cartan matrices…

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…

In this paper we describe six pencils of K3-surfaces which have large Picard-Number and contain precisely five singular fibers: four have A-D-E singularities and one is non-reduced. In particular we describe these surfaces as cyclic…

Let X be a complex projective K3 surface, and let T(X) be its transcendental lattice; the characteristic polynomials of the isometries of T(X) induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic…

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…

If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between $0$ and $18$. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel…

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…