A 4₃ configuration of lines and conics in ℙ⁵
Studying the connection between the title configuration and Kummer surfaces we write explicit quadratic equations for the latter. The main results are presented in Theorems 8 and 16.
A Foruier-Mukai transform for stable bundles on K3 surfaces.
A new family of surfaces with and
A new proof of the existence of Kähler-Einstein metrics on A3, II.
A new proof of the existence of Kähler-Einstein metrics on K3, I.
A note on Donaldson polynomials for K3 surfaces.
A note on Z/p/-actions on K3 surfaces in odd characteristic p.
Abelian varieties associated to certain K3 surfaces
Around real Enriques surfaces.
We present a brief overview of the classification of real Enriques surfaces completed recently and make an attempt to systemize the known classification results for other special types of surfaces. Emphasis is also given to the particular tools used and to the general phenomena discovered; in particular, we prove two new congruence type prohibitions on the Euler characteristic of the real part of a real algebraic surface.
Classification des varietes coplexes projectives de dimension trois dont une section hyperplane générale est une surface d'Enriques.
Classification of Buchsbaum subvarieties of codimension 2 in projective space.
Classification of non-rigid families of K3 surfaces and a finiteness theorem of Arakelov type.
Compactifications of the period space of Enriques surfaces.
Compactifications of the period space of Enriques surfaces. II.
Configurations of In Fibers on Elliptic K 3 Surface.
Cubic points on cubic curves and the Brauer-Manin obstruction on K3 surfaces
Density of rational points on elliptic surfaces
Differential Equations associated to Families of Algebraic Cycles
We develop a theory of differential equations associated to families of algebraic cycles in higher Chow groups (i.e., motivic cohomology groups). This formalism is related to inhomogenous Picard–Fuchs type differential equations. For a families of K3 surfaces the corresponding non–linear ODE turns out to be similar to Chazy’s equation.
Double integrals on a weighted projective plane and Hilbert modular functions for ℚ (√5)
The aim of this paper is to give an explicit extension of classical elliptic integrals to the Hilbert modular case for ℚ (√5). We study a family of Kummer surfaces corresponding to the Humbert surface of invariant 5 with two complex parameters. Our Kummer surface is given by a double covering of the weighted projective space ℙ(1:1:2) branched along a parabola and a quintic curve. The period mapping for our family is given by double integrals of an algebraic function on chambers coming from an arrangement...
Elementary transformations of Dynkin graphs and singularities on quartic surfaces.