Related papers: Genus Zero Complete Maximal Maps and Maxfaces with…
Maximal green sequences are particular sequences of quiver mutations appearing in the context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting maximal green sequences as paths in various natural posets arising…
We prove the existence of an effective universal upper bound for the order of any integral periodic orbit of any integral algebraic dynamical system in a fixed ambient space. Using this, we demonstrate the decidability of periodicity in…
In this work, we investigate the optimal map-making technique for the linear system $d=Ax+n$ while carefully taking into account singularities that may come from either the covariance matrix $C = \langle nn^t \rangle$ or the main matrix…
We prove that the finiteness of a finitely generated category of irreducible algebraic varieties over a field of characteristic zero is decidable. We also obtain a Burnside finiteness criterion for such a category, with applications to…
Let $X=\mathbb{D}/\Gamma$ be an arbitrary Riemann surface. We establish a necessary and sufficient criterion for $[f]\in T(X)$ to have a Teichm\"uller-type extremal map.
For any given natural $d\ge 1$ we provide examples of rational self-maps of complex projective plane $\pp^2$ of degree $d$ without (holomorphic) fixed points. This makes a contrast with the situation in one dimension. We also prove that the…
Given any finite set of nonnegative integers, there exists a closed convex set whose facial dimension signature coincides with this set of integers, that is, the dimensions of its nonempty faces comprise exactly this set of integers. In…
We refine Osserman's argument on the exceptional values of the Gauss map of algebraic minimal surfaces. This gives an effective estimate for the number of exceptional values and the totally ramified value number for a wider class of…
It is well known that any triangulation of a marked surface produces a quiver. In this paper we will provide a triangulation for orientable surfaces of genus $n$ with an arbitrary number interior marked points (called punctures) whose…
We provide upper bounds for the cardinality of the value set of a polynomial map in several variables over a finite field. These bounds generalize earlier bounds for univariate polynomials.
In this paper we obtain the extended genus field of a global field. First we define the extended genus field of a global function field and we obtain, via class field theory, the description of the extended genus field of an arbitrary…
In this paper, we show that a closed manifold $M^{n+1} (n \geq 7)$ endowed with a $C^\infty$-generic (Baire sense) metric contains infinitely many singular minimal hypersurfaces with optimal regularity. Moreover, for $2 \leq n \leq 6$, our…
We say that a subset of $\mathbb{P}^n(\mathbb{R})$ is maximally singular if its contains points with $\mathbb{Q}$-linearly independent homogenous coordinates whose uniform exponent of simultaneous rational approximation is equal to $1$, the…
We study minimal vertex covers and maximal matchings on trees. We pay special attention to the corresponding backbones i.e. these vertices that are occupied and those that are empty in every minimal vertex cover (resp. these egdes that are…
Effective bounds for the finite number of surjective holomorphic maps between canonically polarized compact complex manifolds of any dimension with fixed domain are proven. Both the case of a fixed target and the case of varying targets are…
A smooth map having only fold singularities is called a fold-map. We will give effective conditions for a continuous map to be homotopic to a fold-map from the viewpoint of the homotopy principle.
It is proved that if $D$ is a $UFD$ and $R$ is a $D$-algebra, such that $U(R)\cap D\neq U(D)$, then $R$ has a maximal subring. In particular, if $R$ is a ring which either contains a unit $x$ which is not algebraic over the prime subring of…
The structure of maximal faces of the cone of completely positive matrices is still not well understood in higher dimensions, mainly due to the lack of a general characterization of extreme exposed rays of the copositive cone beyond small…
Suppose $M$ is a complete, embedded minimal surface in $\mathbb{R}^3$ with an infinite number of ends, finite genus and compact boundary. We prove that the simple limit ends of $M$ have properly embedded representatives with compact…
The rank of a graph is defined to be the rank of its adjacency matrix. A graph is called reduced if it has no isolated vertices and no two vertices with the same set of neighbors. A reduced graph $G$ is said to be maximal if any reduced…