Related papers: On complex surfaces with definite intersection for…

These notes are an introduction to and an overview of the theory of algebraic surfaces over algebraically closed fields of positive characteristic. After some background in characteristic-p-geometry, we sketch the Kodaira-Enriques…

The aim of this paper is to study lattice properties of the sharp partial order for complex matrices having index at most 1. We investigate the down-set of a fixed matrix $B$ under this partial order via isomorphisms with two different…

A lattice is called well-rounded, if its lattice vectors of minimal length span the ambient space. We show that there are interesting connections between the existence of well-rounded sublattices and coincidence site lattices (CSLs).…

The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…

Let $X$ be a quadratic vector field with a center whose generic orbits are algebraic curves of genus one. To each $X$ we associate an elliptic surface (a smooth complex compact surface which is a genus one fibration). We give the list of…

We classify smooth surfaces whose higher cohomologies of i-forms for all i vanish. We show that if such a surface is not affine, then it has essentially two possibilities.

In the present article, we provide examples of fake quadrics, that is, minimal complex surfaces of general type with the same numerical invariants as the smooth quadric in $\PP ^3$ which are quotients of the bidisc by an irreducible lattice…

We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…

A tiling (edge-to-edge) of the plane is a family of tiles that cover the plane without gaps or overlaps. Vertex figure of a vertex in a tiling to be the union of all edges incident to that vertex. A tiling is $k$-vertex-homogeneous if any…

We prove a correspondence theorem for singular tropical surfaces in real three space, which recovers singular algebraic surfaces in an appropriate toric three-fold that tropicalize to a given singular tropical surface. Furthermore, we…

Let Y be a surface with only finitely many singularities all of which are cusps. A set of cusps on Y is called three-divisible, if there is a cyclic global triple cover of Y branched precisely over these cusps. The aim of this note is to…

Pure gauge lattice QCD at arbitrary D is considered. Exact integration over link variables in an arbitrary D-volume leads naturally to an appearance of a set of surfaces filling the volume and gives an exact expression for functional of…

Let X be a K3 surface with a polarization H of degree H^2=2rs and with a primitive Mukai vector (r,H,s). The moduli space of sheaves over X with the isotropic Mukai vector (r,H,s) is again a K3 surface Y. We prove that Y\cong X, if Picard…

A surface $\Sigma \subset S^5 \subset \mathbb{C}^3$ is called \emph{special Legendrian} if the cone $0 \times \Sigma \subset \mathbb{C}^3$ is special Lagrangian. The purpose of this paper is to propose a general method toward constructing…

We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the…

We show that if a cubic hypersurface with positive dual defect over the complex number field is not a cone, then either the hypersurface coincides with the secant variety of the singular locus, or the hypersurface contains a linear…

Two arrangements with the same combinatorial intersection lattice but whose complements have different fundamental groups are called a Zariski pair. This work finds that there are at most nine such pairs amongst all ten line arrangements…

The possibility is considered for the formation in optical lattices of a heterogeneous state characterized by a spontaneous mesoscopic separation of the system into the spatial regions with different atomic densities. It is shown that such…

Let $L$ be an $n$-element finite lattice. We prove that if $L$ has strictly more than $2^{n-5}$ congruences, then $L$ is planar. This result is sharp, since for each natural number $n\geq 8$, there exists a non-planar lattice with exactly…

By definition, the intersection of finitely many open sets of any topological space is open. Nachbin observed that, more generally, the intersection of compactly many open sets is open. Moreover, Nachbin applied this to obtain elegant…