O jedné ploše stupně čtvrtého
On a stratification of the moduli of K3 surfaces
In this paper we give a characterization of the height of K3 surfaces in characteristic . This enables us to calculate the cycle classes in families of K3 surfaces of the loci where the height is at least . The formulas for such loci can be seen as generalizations of the famous formula of Deuring for the number of supersingular elliptic curves in characteristic . In order to describe the tangent spaces to these loci we study the first cohomology of higher closed forms.
On Brauer groups of real Enriques surfaces.
On Enriques Surfaces in Characteristic p. II.
On large Picard groups and the Hasse Principle for curves and K3 surfaces
On moduli spaces of semistable sheaves on Enriques surfaces
We describe some one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In the case of a nodal Enriques surface the moduli spaces obtained are reducible for general polarizations. For unnodal Enriques surfaces we show how to reduce the study of moduli spaces of high even rank Gieseker semistable sheaves to low ranks. To prove this we use the method of K. Yoshioka who showed that in the odd rank case, one can reduce to rank...
On the Albanese variety of the moduli space of polarized K3 surfaces.
On the Brill-Noether theory for K3 surfaces
Let (S, H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c 1(E), H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of coherent sheaves of different ranks on S, we prove our main theorem: polarized K3 surface which...
On the distribution of rational points on certain Kummer surfaces
On the Kodaira dimension of the moduli space of K3 surfaces
On the uniqueness of elliptic K3 surfaces with maximal singular fibre
We explicitly determine the elliptic surfaces with section and maximal singular fibre. If the characteristic of the ground field is different from , for each of the two possible maximal fibre types, and , the surface is unique. In characteristic the maximal fibre types are and , and there exist two (resp. one) one-parameter families of such surfaces.
On total reality of meromorphic functions
We show that, if a meromorphic function of degree at most four on a real algebraic curve of an arbitrary genus has only real critical points, then it is conjugate to a real meromorphic function by a suitable projective automorphism of the image.
On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors
We extend results on generic strange duality for surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized .
Ordinary reduction of K3 surfaces
Let X be a K3 surface over a number field K. We prove that there exists a finite algebraic field extension E/K such that X has ordinary reduction at every non-archimedean place of E outside a density zero set of places.