Related papers: On Eckl's pseudo-effective reduction map
We study how the number $c(X)$ of components of a graph $X$ can be expressed through the number and properties of the components of a quotient graph $X/\sim.$ We partially rely on classic qualifications of graph homomorphisms such as…
Let $\mathbf{O}(\mathbb{F})$ be the split octonion algebra over an algebraically closed field $\mathbb{F}$. For positive integers $k_1, k_2\geq 2$, we study surjectivity of the map $A_1(x^{k_1}) + A_2(y^{k_2}) \in…
Let $K$ be any field, and let $E$ be any graph. We explicitly construct the projective resolution of simple left modules over the Leavitt path algebra $L_K(E)$ associated to cycles and irreducible polynomials. Then we study the dimension of…
The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of…
We prove that, if X is a variety over an uncountable algebraically closed field k of characteristic zero, then any irreducible exceptional divisor E on a resolution of singularities of X which is not uniruled, belongs to the image of the…
Let $E/\mathbb Q(t)$ be an elliptic curve and let $t_0 \in \mathbb Q$ be a rational number for which the specialization $E_{t_0}$ is an elliptic curve. Given a subgroup $M$ of $E(\mathbb Q(t))$ with mild conditions and $t_0 \in \mathbb Q$…
A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
Let $C/K$ be a smooth plane quartic over a discrete valuation field. We characterize the type of reduction (i.e. smooth plane quartic, hyperelliptic genus 3 curve or bad) over $K$ in terms of the existence of a special plane quartic model…
The minimum k-partition problem is a challenging combinatorial problem with a diverse set of applications ranging from telecommunications to sports scheduling. It generalizes the max-cut problem and has been extensively studied since the…
For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…
In this paper, we studied the map defined by a non-very ample line bundle on some special irregular varieties. As to this topic, it is well known that for a line bundle $L$ on an Abelian variety $A$, the linear system $|2L|$ is base point…
Let $\mathcal{O}_K$ be a Henselian discrete valuation domain with field of fractions $K$. Assume that $\mathcal{O}_K$ has algebraically closed residue field $k$. Let $E/K$ be an elliptic curve with additive reduction. The semi-stable…
A {\em cyclic graph} is a graph with at each vertex a cyclic order of the edges incident with it specified. We characterize which real-valued functions on the collection of cubic cyclic graphs are partition functions of a real vertex model…
Let $K$ be a number field with ring of integers $\mathcal{O}_K$. We describe and classify finite, flat, and linearly reductive subgroup schemes of $\mathrm{SL}_2$ over $\mathrm{Spec}\:\mathcal{O}_K$. We also establish finiteness results for…
In the design and analysis of political redistricting maps, it is often useful to be able to sample from the space of all partitions of the graph of census blocks into connected subgraphs of equal population. There are influential Markov…
We present counting methods for some special classes of multivariate polynomials over a finite field, namely the reducible ones, the s-powerful ones (divisible by the s-th power of a nonconstant polynomial), and the relatively irreducible…
A conjecture of Colliot-Th\'{e}l\`{e}ne predicts that for a smooth projective variety $X$ over a finite extension $k$ of $\mathbb{Q}_p$ the kernel of the Albanese map $\text{CH}_0(X)^{\text{deg}=0}\to Alb_X(k)$ is the direct sum of a…
Many problems across computer vision and the natural sciences require the analysis of spherical data, for which representations may be learned efficiently by encoding equivariance to rotational symmetries. We present a generalized spherical…
Given a positive real Hermitian holomorphic line bundle L over a smooth real projective manifold X, the space of real holomorphic sections of the bundle L^d inherits for every positive integer d a L^2 scalar product which induces a Gaussian…