Related papers: The automorphism groups of Kummer surfaces in char…
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 discuss K3 surfaces in characteristic two that contain the Kummer configuration formed by smooth rational curves on it.
Every indefinite binary form occurs as the Picard lattice of some K3-surface. The group of its isometries, or automorphs, coincides with the automorphism group of the K3-surface, but only up to finite groups. The classical theory of…
In this paper we classify curves of genus 2 with group of automorphisms isomorphic to D_8 or D_12 over an arbitrary field k (of characteristic different from 2 in the D_8 case and from 2 and 3 in the D_{12} case) up to k-isomorphism. As 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 the case of a $K3$ surface of Picard rank two such that…
We study the geometry of the K3 surfaces $X$ with a finite number automorphisms and Picard number $\geq 3$. We describe these surfaces classified by Nikulin and Vinberg as double covers of simpler surfaces or embedded in a projective space.…
We study the birational geometry of the Kummer surfaces associated to the Jacobian varieties of genus two curves, with a particular focus on fields of characteristic two. In order to do so, we explicitly compute a projective embedding of…
To a pair of elliptic curves, one can naturally attach two K3 surfaces: the Kummer surface of their product and a double cover of it, called the Inose surface. They have prominently featured in many interesting constructions in algebraic…
We construct a K3 surface over an algebraically closed field of characteristic 2 which contains two sets of 21 disjoint smooth rational curves such that each curve from one set intersects exactly 5 curves from the other set. This…
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 is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good…
A generalized Kummer surface $X$ obtained as the quotient of an abelian surface by a symplectic automorphism of order 3 contains a $9\mathbf{A}_{2}$-configuration of $(-2)$-curves. Such a configuration plays the role of the…
We classify supersingular and classical Enriques surfaces with finite automorphism group in characteristic 2 into 8 types according to their dual graphs of all $(-2)$-curves (nonsigular rational curves). We give examples of these Enriques…
Kummer surfaces are special quartic surfaces that admit $16$ nodes. The automorphisms of K3 Kummer surfaces are rich and complicated. Based on the results of Keum and Kond\=o, and as a continuation of the recent result by He and Yang, we…
It is known that an automorphism group of a K3 surface with Picard number two is either infinite cyclic group or infinite dihedral group if it is infinite. In this paper, we study the generators of an automorphism group. We use the…
We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic automorphism of order 16. The automorphism acts on the second cohomology group with integer coefficients and we compute the invariant sublattice for the action. We…
We introduce Kummer surfaces X=Km(CxC) with the group scheme G=mu_2 acting on the self-product of the rational cuspidal curve in characteristic two. The resulting quotients are normal surfaces having a configuration of sixteen rational…
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 calculate the automorphism group of certain Enriques surfaces. The Enriques surfaces that we investigate include very general $n$-nodal Enriques surfaces and very general cuspidal Enriques surfaces. We also describe the action of the…
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…