Related papers: Zariski K3 surfaces

In this paper we construct new indecomposable motivic cycles in the group $H^3_{\mathcal M}(X,{\mathbb Q}(2))$ where X is a degree 2 K3 surface. This generalizes our construction in [Sre22] for Kummer surfaces of Abelian surfaces as well as…

We explicitly construct the Kummer variety associated to the Jacobian of a hyperelliptic curve of genus 3 that is defined over a field of characteristic not equal to 2 and has a Weierstra{\ss} point defined over the same field. We also…

In this paper, we characterize smooth projective surfaces on which every integral pseudoeffective divisor has an integral Zariski decomposition.

We show that there exist a complex projective K3 surface $X$ and an automorphism of the complex numbers $\sigma$ such that the conjugate K3 surface $X^\sigma$ is a non-isomorphic Fourier-Mukai partner of $X$.

For $\mathbb Z_3$-orbifold limits of K3, we provide a counterpart to the extensive studies by Nikulin and others of the geometry and symmetries of classical Kummer surfaces. In particular, we determine the group of holomorphic symplectic…

In arXiv:1008.3825, Totaro gave examples of a K3 surface such that its automorphism group is not commensurable with an arithmetic group, answering a question of Mazur. We give examples of rational surfaces with the same property. Our…

In this paper we give an asymptotic bound of the cardinality of Zariski multiples of particular plane singular curves. These curves have only nodes and cusps as singularities and are obtained as branched curves of ramified covering of the…

This is a survey on Zariski equisingularity. We recall its definition, main properties, and a variety of applications in Algebraic Geometry and Singularity Theory. In the first part of this survey, we consider Zariski equisingular families…

Let k=F_q be a finite field of characteristic 2. A genus 3 curve C/k has many involutions if the group of k-automorphisms admits a C_2\times C_2 subgroup H (not containing the hyperelliptic involution if C is hyperelliptic). Then C is an…

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 prove that any hyper-K\"{a}hler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm{K}3^{[3]}$-type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic…

We construct a lot of K3 surface automorphisms of positive entropy having rotation domains of ranks 1 and 2. To carry out this construction, we first lay theoretical foundations concerning equivariant linearization of nonlinear maps under…

We show that the moduli space of $U\oplus \langle -2k \rangle$-polarized K3 surfaces is unirational for $k \le 50$ and $k \notin \{11,35,42,48\}$, and for other several values of $k$ up to $k=97$. Our proof is based on a systematic study of…

We test R. van Luijk's method for computing the Picard group of a $K3$ surface. The examples considered are the resolutions of Kummer quartics in $\bP^3$. Using the theory of abelian varieties, in this case, the Picard group may be computed…

We consider modular properties of nodal curves on general $K3$ surfaces. Let $\mathcal{K}_p$ be the moduli space of primitively polarized $K3$ surfaces $(S,L)$ of genus $p\geqslant 3$ and $\mathcal{V}_{p,m,\delta}\to \mathcal{K}_p$ be the…

Given d in IN, we prove that all smooth K3 surfaces (over any field of characteristic p other than 2,3) of degree greater than 84d^2 contain at most 24 rational curves of degree at most d. In the exceptional characteristics, the same bounds…

We compute the Zariski closure of the Kontsevich-Zorich monodromy groups arising from certain square tiled surfaces that are geometrically motivated. Specifically we consider three surfaces that emerge as translation covers of platonic…

Let S be a K3 surface that admits a non-symplectic automorphism $\rho$ of order 3. We divide $S\times \mathbb{P}^1$ by $\rho\times\psi$ where $\psi$ is an automorphism of order 3 of $\mathbb{P}^1$. There exists a threefold ramified cover of…

We study the symplectic action of the group (Z/2Z)^2 on a K3 surface X: we describe its action on H^2(X,Z) and the maps induced in cohomology by the rational quotient maps; we give a lattice-theoretic characterization of the resolution of…

We study isogeny relations between K3 surfaces and Kummer surfaces. Specifically, we prove a Torelli-type theorem for the existence of rational maps from K3 surfaces to Kummer surfaces, and a Kummer sandwich theorem for K3 surfaces with…