相关论文: The 2-divisibility of divisors on K3 surfaces in c…

We construct, on a supersingular K3 surface with Artin invariant 1 in characteristic 2, a set of 21 disjoint smooth rational curves and another set of 21 disjoint smooth rational curves such that each curve in one set intersects exactly 5…

We describe the possible 3-divisible $A_2^n$ configurations of smooth rational curves on K3 surfaces in characteristic 3 and fully classify the resulting triple covers.

We show the existence of 112 non-singular rational curves on the supersingular K3 surface with Artin invariant 1 in characteristic 3 by several ways. Using these rational curves, we have a $(16)_{10}$-configuration and a $(280_{4},…

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…

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…

A K3 surface over a number field has infinitely many rational points over a finite field extension. For K3 surfaces of degree 2, arising as double covers of $\mathbb{P}^2$ branched along a smooth sextic curve, we give a bound for the degree…

We determine all possible configurations of rational double points on complex normal algebraic K3 surfaces, and on normal supersingular K3 surfaces in characteristic p > 19.

We show that every supersingular K3 surface in characteristic 5 with Artin invariant less than or equal to 3 is unirational.

A complex K3 surface or an algebraic K3 surface in characteristics distinct from $2$ cannot have more than $16$ disjoint nodal curves.

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…

Given a K3 surface X over a field of characteristic p, Artin conjectured that if X is supersingular (meaning infinite height) then its Picard rank is 22. Along with work of Nygaard-Ogus, this conjecture implies the Tate conjecture for K3…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

We give a 1-dimensional family of classical and supersingular Enriques surfaces in characteristic 2 covered by the supersingular K3 surface with Artin invariant 1. Moreover we show that there exist 30 nonsingular rational curves and ten…

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 study complex algebraic K3 surfaces of Picard ranks 11,12, and 13 of finite automorphism group that admit a Jacobian elliptic fibration with a section of order two. We prove that the K3 surfaces admit a birational model isomorphic to a…

We introduce an inseparable version of Kummer surfaces. It is defined as a supersingular K3 surface in characteristic 2 with 16 smooth rational curves forming a certain configuration and satisfying a suitable divisibility condition. The…

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 construct Zariski K3 surfaces of Artin invariant 1, 2 and 3 in many characteristics. In particular, we prove that any supersingular Kummer surface is Zariski if the characteristic is not congruent to 1 modulo 12. Our methods combine…

Using the properties of generalized Fibonacci numbers, we determine the automorphism groups of some K3 surfaces with Picard number 2. Conversely, using the automorphisms of K3 surfaces with Picard number 2, we prove the criterion for a…

In characteristic $p=0$ or $p>5$, we show that a K3 surface with an order 60 automorphism is unique up to isomorphism. As a consequence, we characterize the supersingular K3 surface with Artin invariant 1 in characteristic $p=11$ (mod 12)…