Related papers: Local boundedness of Catlin q-type
Pach showed that every $d+1$ sets of points $Q_1,\dotsc,Q_{d+1} \subset \mathbb{R}^d$ contain linearly-sized subsets $P_i\subset Q_i$ such that all the transversal simplices that they span intersect. We show, by means of an example, that a…
This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…
The Danielewski hypersurfaces are the hypersurfaces $X_{Q,n}$ in $\mathbb{C}^3$ defined by an equation of the form $x^ny=Q(x,z)$ where $n\geq1$ and $Q(x,z)$ is a polynomial such that $Q(0,z)$ is of degree at least two. They were studied by…
For any prime $p\ge 5$, we show that generic hypersurface $X_p\subset\mathbb{P}^p$ defined over $\mathbb{Q}$ admits a non-trivial rational dominant self-map of degree $>1$, defined over $\bar{\mathbb{Q}}$. A simple arithmetic application of…
For a variety of finite groups $\mathbf H$, let $\overline{\mathbf H}$ denote the variety of finite semigroups all of whose subgroups lie in $\mathbf H$. We give a characterization of the subsets of a finite semigroup that are pointlike…
We completely characterize $L^p-L^q$ boundedness of two classes of Forelli-Rudin type operators on the unit ball of $\mathbb{C}^n$ for all $(p, q)\in [1, \infty]\times [1, \infty]$. The results are not only a complement to some previous…
Subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the results of [LR95] to the case of extensions with…
This paper is devoted to the study of metric subregularity and strong subregularity of any positive order $q$ for set-valued mappings in finite and infinite dimensions. While these notions have been studied and applied earlier for $q=1$…
We use the cylindrical homomorphism and a geometric construction introduced by J. Lewis to study the Lawson homology groups of certain hypersurfaces $X\subset \mathbb{P}^{n+1}$ of degree $d\leq n+1$. As an application, we compute the…
In a recent paper by Cook, et al., which introduced the concept of unexpected plane curves, the focus was on understanding the geometry of the curves themselves. Here we expand the definition to hypersurfaces of any dimension and, using…
We introduce a family of local ranks DQ depending on a finite set Q of pairs of the form (\varphi(x,y),q(y)) where \varphi(x,y) is a formula and q(y) is a global type. We prove that in any NSOP1 theory these ranks satisfy some desirable…
Generalising an example by Girondo and Wolfart, we use finite group theory to construct Riemann surfaces admitting two or more regular dessins (i.e. orientably regular hypermaps) with automorphism groups of the same order, and in many cases…
Let $k$ be a field of characteristic not 2 or 3. We establish polynomial lower bounds on the ambient dimension $N$ for an intersection $X\subset\mathbb{P}^N$ of quadrics, cubics and quartics to have a dense collection of solvable points,…
On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this…
We establish an effective Bertini-type theorem for hypersurfaces $X_f \colon f = 0$ defined over a finite field $k$ for which $f$ has no linear factors over the algebraic closure $\overline{k}$. Given a line $L$ defined over $k$ and a…
Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, Physics, Chemistry or Economy. In addition, QP mappings are a…
We point out an explicit connection between graphs drawn on compact Riemann surfaces defined over the field $\bar{\mathbb{Q}}$ of algebraic numbers --- so-called Grothendieck's {\it dessins d'enfants} --- and a wealth of distinguished…
In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's…
We define the unit circle for global function fields. We demonstrate that this unit circle (endearingly termed the \emph{$q$-unit circle}, after the finite field $\mathbb{F}_q$ of $q$ elements) enjoys all of the properties akin to the…
For any affine hypersurface defined by a complete symmetric polynomial in $k\geq 3$ variables of degree $m$ over the finite field $\mathbb{F}_{q}$ of $q$ elements, a special case of our theorem says that this hypersurface has at least…