Related papers: Soft planes and groups
We describe the behaviour of a free reduced plane projective curve with respect to the deletion, respectively addition, of a smooth conic. These results apply in particular to conic-line arrangements. We present some obstructions to the…
Let $G$ be a group. The intersection graph of subgroups of $G$, denoted by $\mathscr{I}(G)$, is a graph with all the proper subgroups of $G$ as its vertices and two distinct vertices in $\mathscr{I}(G)$ are adjacent if and only if the…
We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the…
We classify closed curves isomorphic to the affine line in the complement of a smooth rational projective plane conic Q. Over a field of characteristic zero, we show that up to the action of the subgroup of the Cremona group of the plane…
In this paper, we investigate the question of triviality of the rational Chow groups of complete intersections in projective spaces and obtain improved bounds for this triviality to hold. Along the way, we study the dimension and…
We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.
In this manuscript the idea of soft convex structures is given and some of their properties are investigated. Also, soft convex sets, soft concave sets and soft convex hull operator are defined and their properties are studied. Moreover,…
We first describe the tangent space to the affine flag manifold associated to a simple algebraic group over $\mathbb{C}$ at the distinguished point starting from standard definitions. We then construct projective lines in the affine flag…
We prove that a system of particles in the plane, interacting only with a certain hard-core constraint, undergoes a fluid/solid phase transition.
In any dimension at least five we construct examples of closed smooth manifolds with the following properties: 1) they have neither real projective nor flat conformal structures; 2) their fundamental group is a non-elementary Gromov…
Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…
It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces,…
This paper is dedicated to the problem of infinite transitivity for algebraically generated automorphism groups of the affine plane. We provide a necessary and sufficient condition of infinite transitivity for a large family of subgroups…
We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…
We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them…
We discuss solutions of several questions concerning the geometry of conformal planes.
The order in which plane-filling curves visit points in the plane can be exploited to design efficient algorithms. Typically, the curves are useful because they preserve locality: points that are close to each other along the curve tend to…
A unital $\ell$-group is an abelian group equipped with a translation invariant lattice-order and with a distinguished strong unit, i.e. an element whose positive integer multiples eventually dominate every element of $G$.If $X$ is a…
The aim of this paper is twofold: First we classify all abstract light dual multinets of order $6$ which have a unique line of length at least two. Then we classify the weak projective embeddings of these objects in projective planes over…
We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.