Related papers: Kinematic generation of Darboux cyclides
We characterise the quartic (i.e. 4-regular) multigraphs with the property that every edge lies in a triangle. The main result is that such graphs are either squares of cycles, line multigraphs of cubic multigraphs, or are obtained from…
In this paper we examine curves defined over a field of characteristic 2 which are $(\ZZ/2\ZZ)^2$-covers of the projective line. In particular, we prove which 2-ranks occur for such curves of a given genus and where possible we give…
We construct and study a family of double-periodic almost entire solutions of the maximal surface equation. The solutions are parameterized by a submanifold of $3\times 3$-matrices (the so-called generating matrices). We show that the…
We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality.
This paper presents an algebraic construction of families of unitary matrices that achieve full diversity. They are obtained as subsets of cyclic division algebras.
This article computes the Galois groups of congruence covers arising in the context of certain hyperbolic triangle groups. As a consequence of this computation, the genera of the respective curves are deduced.
There is a natural duality between line congruences in $\mathbb{R}^3$ and surfaces in $\mathbb{R}^4$ that sends principal lines into asymptotic lines. The same correspondence takes the discriminant curve of a line congruence into the…
Double circulant matrices are introduced and studied. A formula to compute the rank r of a double circulant matrix is exhibited; and it is shown that any consecutive r rows of the double circulant matrix are linearly independent. As a…
We compute explicit bases for the de Rham cohomology of cyclic covers of the projective line defined over an algebraically closed field of characteristic $p\geq 0$. For both Kummer and Artin-Schreier extensions, we describe precise…
We present a method for calculating the Brauer group of a surface given by a diagonal equation in the projective space. For diagonal quartic surfaces with coefficients in Q we determine the Brauer groups over Q and Q(i).
We introduce a new class of surfaces in Euclidean $3$-space, called surfaces of osculating circles, using the concept of osculating circle of a regular curve. These surfaces contain a uniparametric family of planar lines of curvature. In…
We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…
This note provides the construction of a three-variable family of cohomology classes arising from diagonal cycles on a triple product of towers of modular curves, and proves a reciprocity law relating it to the three variable triple-product…
We study nodal quintic surfaces with an even set of 16 nodes as analogues of singular Kummer surfaces. The interpretation of the natural double cover of an even 16-nodal quintic as a certain Fano variety of lines could be viewed as a…
We point out a link between two surfaces which have appeared recently in the literature: the surface of cuboids and the Schoen surface. Both surfaces give rise to a surface with q=4, whose canonical map is 2-to-1 onto an intersection of 4…
The minimal resolution of the degree four cyclic cover of the plane branched along a GIT stable quartic is a K3 surface with a non symplectic action of Z_4. In this paper we study the geometry of the one dimensional family of K3 surfaces…
A study of triangulations of cycles in the Cayley diagrams of finitely generated groups leads to a new geometric characterization of hyperbolic groups.
In this paper is studied the behavior of lines of curvature near umbilic points that appear generically on surfaces depending on two parameters.
We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a…
In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the…