Related papers: Stabilization of monomial maps

We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get that a certain natural two-dimensional extension of the classical one-dimensional…

Let $X$ be a normal projective variety and $f:X\to X$ a non-isomorphic polarized endomorphism. We give two characterizations for $X$ to be a toric variety. First we show that if $X$ is $\mathbb{Q}$-factorial and $G$-almost homogeneous for…

For any smooth compact manifold $W$ of dimension at least two we prove that the classifying spaces of its group of diffeomorphisms which fix a set of $k$ points or $k$ embedded disks (up to permutation) satisfy homology stability. The same…

We construct a moduli space of stable pairs over a smooth projective variety, parametrizing morphisms from a fixed coherent sheaf to a varying sheaf of fixed topological type, subject to a stability condition. This generalizes the notion…

Suppose that $f: Y\to X$ is a proper, dominant, tamely ramified morphism of algebraic surfaces, over a perfect field. We show that it is possible to perform sequences of monoidal transforms $Y'\to Y$ and $X'\to X$ to obtain an induced…

We prove an equidistribution result for iterated preimages of curves by a large class of rational maps $f:\mathbb{CP}^2\dashrightarrow\mathbb{CP}^2$ that cannot be birationally conjugated to algebraically stable maps. The maps, which…

For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, namely a stable subgroup and a Morse or strongly quasiconvex subgroup. Durham and Taylor defined…

For a Riemannian polyhedra, we study the geometry of the unit ball for the unidimensional stable norm (stable ball). In the case of a unidimensional Riemannian polyhedra (graph), we show that the stable ball is a polytope whose vertices are…

We consider the problem of deciding whether the solution sets of a parametrized polynomial system are toric in the sense that they admit a monomial parametrization. We focus on vertically parametrized systems, which are sparse systems where…

For a surjective self-morphism on a projective variety defined over a number field, we study the preimages question, which asks if the set of rational points on the iterated preimages of an invariant closed subscheme eventually stabilize.…

Let $M$ be a compact Riemannian manifold, and let $G$ be a compact simple Lie group with bi-invariant metric that is not $\operatorname{Sp}(n)$ for $n \geq 8$, $E_{8}$, $F_{4}$, or $G_{2}$. We show that the singular set of any stable…

We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold $(M^n,g)$ of dimension $n>2$ to any closed, non-aspherical manifold $N$ containing no stable minimal two-spheres. In particular,…

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of…

Every $n th$ order monic polynomial corresponds $n$-dimensional vector. If the given polynomial is stable that is all its roots lie in the open left half plane it is said to be Hurwitz polynomial and the corresponding vector is called…

We prove that, if $n\geq 3$, a singular foliation $\mathcal{F}$ on $\mathbb P^n$ which can be written as pull-back, where $\mathcal{G}$ is a foliation in $ {\mathbb P^2}$ of degree $d\geq2$ with one or three invariant lines in general…

Let $X$ be a smooth projective surface over an algebraically closed field $k$ of characteristic $p> 0$ with $\Omega_{X}^{1}$ semistable and $\mu(\Omega_{X}^{1})>0$. For any semistable (resp. stable) bundle $W$ of rank $r$, we prove that…

The best-known way of stabilizing textures is by Skyrme-like terms, but another possibility is to use gauge fields. The semilocal vortex may be viewed as an example of this, in two spatial dimensions. In three dimensions, however, the idea…

We study the pullback maps on cohomology groups for equivariant rational maps (i.e., monomial maps) on toric varieties. Our method is based on the intersection theory on toric varieties. We use the method to determine the dynamical degrees…

We show that for any stable sheaf $E$ of slope $> 2g-1$ on a smooth, projective curve of genus $g$, the associated Picard sheaf $\hat{E}$ on the Picard variety of the curve is stable. We introduce a homological tool for testing…

By varying a parameter of a one-dimensional piecewise smooth map, stable periodic orbits are observed. In this paper, complete analytic characterization of these stable periodic orbits is obtained. An interesting relationship between the…