Related papers: Classical curves via one-vertex maps

Fialowski and Schlichenmaier constructed examples of global deformations of Lie algebras of vector fields from deforming the underlying variety. We formulate their approach in a conceptual way. Namely, we construct a stack of deformations…

Given smooth, projective, geometrically integral algebraic curves $X$ and $Y$ defined over a number field $K$, assuming that there is a non-constant $K$-morphism $\varphi \colon X \to Y$, we give an upper bound on the minimum of the degrees…

A metrized complex of algebraic curves is a finite metric graph together with a collection of marked complete nonsingular algebraic curves, one for each vertex, the marked points being in bijection with incident edges. We establish a…

In this article, we shall derive by elementary calculations the Gauss map, spherical image, Weingarten map and the curvatures at identity of the special linear group, that is, the matrices of determinant 1. We could not find any reference…

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of…

We investigate the Jacobian decomposition of some algebraic curves over finite fields with genus $4$, $5$ and $10$. As a corollary, explicit equations for curves that are either maximal or minimal over the finite field with $p^2$ elements…

The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…

We construct an arithmetic analogue of the quantum local systems on the moduli of curves, and study its basic structure. Such an arithmetic local system gives rise to a uniform way of assigning a Galois cohomology class of the first…

A characterization is given for directed graphs that yield graph $C^*$-algebras with continuous trace. This is established for row-finite graphs with no sources first using a groupoid approach, and extended to the general case via the…

Given a smooth curve, the canonical representation of its automorphism group is the space of global holomorphic differential 1-forms as a representation of the automorphism group of the curve. In this paper, we study an explicit set of…

For each prime number $\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order…

The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…

We prove that any geometrically connected curve $X$ over a field $k$ is an algebraic $K(\pi,1)$, as soon as its geometric irreducible components have nonzero genus. This means that the cohomology of any locally constant constructible…

Dessin d'Enfants on elliptic curves are a powerful way of encoding doubly-periodic brane tilings, and thus, of four-dimensional supersymmetric gauge theories whose vacuum moduli space is toric, providing an interesting interplay between…

In this paper we investigate complex uniruled varieties $X$ whose rational curves of minimal degree satisfy a special property. Namely, we assume that the tangent directions to such curves at a general point $x\in X$ form a linear subspace…

Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of…

The aim of this paper is to classify reduction types of algebraic curves. Reduction types capture the discrete invariants of fibres in one-dimensional families of curves, and they have been described in genus 1, 2 and 3. For fixed genus…

In the mid-1990s, two groups of authors independently obtained classifications of vertex-transitive graphs whose order is a product of two distinct primes. In the intervening years it has become clear that there is additional information…

We investigate approximations of the vertex coupling on a star-shaped graph by families of operators with singularly scaled rank-one interactions. We find a family of vertex couplings, generalizing the $\delta'$-interaction on the line, and…