Related papers: On K3 surfaces which dominate Kummer surfaces

We study the virtual geometry of the moduli spaces of curves and sheaves on K3 surfaces in primitive classes. Equivalences relating the reduced Gromov-Witten invariants of K3 surfaces to characteristic numbers of stable pairs moduli spaces…

Strange duality is shown to hold over generic $K3$ surfaces in a large number of cases. The isomorphism for elliptic $K3$ surfaces is established first via Fourier-Mukai techniques. Applications to Brill-Noether theory for sheaves on $K3$s…

We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which…

We study the derived categories of twisted supersingular K3 surfaces. We prove a derived crystalline Torelli theorem for twisted supersingular K3 surfaces, characterizing Fourier-Mukai equivalences in terms of isomorphisms between their…

We study elliptic K3 surfaces with Mordell Weil rank 0, and which has a 2-torsion section $\sigma$ such that the translation by $\sigma$ gives a Shioda-Inose structure.

In this study, we construct four-dimensional F-theory models with 3 to 8 U(1) factors on products of K3 surfaces. We provide explicit Weierstrass equations of elliptic K3 surfaces with Mordell-Weil ranks of 3 to 8. We utilize the method of…

We prove some cycle relations on moduli of K3 surfaces

We generalize Mukai and Shafarevich's definitions of isogenies between K3 surfaces over $\mathbb{C}$ to an arbitrary perfect field and describe how to construct isogenous K3 surfaces over $\bar{\mathbb{F}}_p$ by prescribing linear algebraic…

With any hyper-K\"ahler variety $K$ of generalized Kummer type is associated via Hodge theory a K3 surface $S_K$. We show how they are related geometrically through a moduli space of sheaves on $S_K$. As a consequence, building…

We study the geometry of B\"uchi's K3 surface showing that the rational points of this surface are Zariski-dense.

In this paper we classify the topological invariants of the possible branch loci of a smooth double cover $f:X\rightarrow Y$ of a K3 surface $Y$. We describe some geometric properties of $X$ which depend on the properties of the branch…

We construct geometric isogenies between three types of two-parameter families of K3 surfaces of Picard rank 18. One is the family of Kummer surfaces associated with Jacobians of genus-two curves admitting an elliptic involution, another is…

We use lattice theory to study the isogeny class of a K3 surface. Starting from isotropic Brauer classes, we construct isogenies via Kneser method of neighboring lattices. We also determine the fields of definition of isogenous K3 surfaces,…

A generalized Kummer surface $X=Km(T,G)$ is the resolution of a quotient of a torus $T$ by a finite group of symplectic automorphisms $G$. We complete the classification of generalized Kummer surfaces by studying the two last groups which…

Let $X\subset \P^5$ be a smooth cubic fourfold. A well known conjecture asserts that $X$ is rational if and only if there an Hodge theoretically associated K3 surface $S$. The surface $S$ can be associated to $X$ in two other different…

We study Fourier-Mukai equivalence of K3 surfaces in positive characteristic and show that the classical results over the complex numbers all generalize. The key result is a positive-characteristic version of the Torelli theorem that uses…

We study the cohomological properties of quasi-canonical lifts of an ordinary K3 surface over a finite field. As applications, we prove a Torelli type theorem for ordinary K3 surfaces over finite fields and establish the Hodge conjecture…

It is known (work of Galluzzi, Lombardo, Dolgachev and Naruki) that there is a unique K3 surface X which corresponds to a genus 2 curve C such that X has a Shioda-Inose structure with quotient birational to the Kummer surface of the…

A generalized Kummer surface $X=Km_{3}(A,G_{A})$ is the minimal resolution of the quotient of a $2$-dimensional complex torus by an order 3 symplectic automorphism group $G_{A}$. A Kummer structure on $X$ is an isomorphism class of pairs…

We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spaces of stable maps and reduction to positive characteristic.