Related papers: Elliptic K3 surfaces with p^n-torsion sections
We study the geometry of exceptional loci of birational contractions of hyper-K\"ahler fourfolds that are of K3$^{[2]}$-type. These loci are conic bundles over K3 surfaces and we determine their classes in the Brauer group. For this we use…
In this paper we give a characterization of the height of K3 surfaces in positive characteristic. This enables us to calculate the cycle classes of the loci in families of K3 surfaces where the height is at least h. The formulas for such…
We survey some aspects of the theory of elliptic surfaces and give some results aimed at determining the Picard number of such a surface. For the surfaces considered, this will be equivalent to determining the Mordell-Weil rank of an…
We prove that the maximal singular fibres of elliptic K3 surfaces have type I_19 and I_14* unless the characteristic of the ground field is 2. In characteristic 2, the maximal singular fibres are I_18 and I_13*. The paper supplements work…
In 2009, Dolgachev-Keum showed that finite groups of tame symplectic automorphisms of K3 surfaces in positive characteristics are subgroups of the Mathieu group of degree 23. In this paper, we utilize lattice-theoretic methods to…
We present a finite set of generators of the automorphism group of a supersingular K3 surface with Artin invariant 1 in characteristic 3.
This note gives an explicit example of transcendental Brauer-Manin obstruction to weak approximation. It has two features which the only previously known example of such obstruction did not have: the class in the Brauer group which is…
We present three interesting projective models of the supersingular K3 surface X in characteristic 5 with Artin invariant 1. For each projective model, we determine smooth rational curves on X with the minimal degree and the projective…
In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one parameter family in terms of those of a particular family of elliptic curves. The Tate conjecture predicts the existence of a…
We show that on every elliptic K3 surface $X$ there are rational curves $(R_i)_{i\in \mathbb{N}}$ such that $R_i^2 \to \infty$, i.e., of unbounded arithmetic genus. Moreover, we show that the union of the lifts of these curves to…
We construct explicitly moduli curves of polarized supersingular K3 surfaces in characteristic 2 with Artin invariant 2. As an application, we detect a "jump" phenomenon in a family of automorphism groups of supersingular K3 surfaces with a…
We discuss some aspects of the behavior of specialization at a finite place of N\'eron-Severi groups of K3 surfaces over number fields. We give optimal lower bounds for the Picard number of such specializations, thus answering a question of…
The more recent paper "Generic strange duality for K3 surfaces" by the authors contains stronger results.
Following Valloni, we study complex projective K3 surfaces having complex multiplication by rings of integers.
Elliptic fibrations of $K3$ surfaces belonging to the Ap\'ery-Fermi pencil ($Y_k$) may have $2$ or $3$-torsion sections defining on $(Y_k)$ automorphisms $\tau$ of order $2$ or $3$. First we consider $Y_{k}/\tau$ \ for some fibrations of…
We give new relations between geometric invariants of $K3$ surfaces with purely non-symplectic automorphisms of order 4 and 6. Our approach is based on a comparison of two methods of computation of formulas for the Euler characteristic of…
This paper aims to establish the geometrical finiteness for the natural isometric actions of (birational) automorphism groups on the hyperbolic spaces for K3 surfaces, Enriques surfaces, Coble surfaces, and irreducible symplectic varieties.…
Using results of our papers [19], [20] and [21] about classification of degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, we classify Picard lattices of Kahlerian K3 surfaces. By classification we understand…
We survey some properties of a class of curves lying on certain elliptic ruled surfaces, studied by A. Treibich and J.L. Verdier in connection with elliptic solitons and KP equations. In particular we discuss their Brill-Noether generality,…
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…