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A compactification of the moduli space of multiple-spin curves
We construct a smooth Deligne–Mumford compactification for the moduli space of curves with an m -tuple of spin structures using line bundles on...
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Implicit Representations of Rational Curves and Surfaces
The subject of this chapter is the implicitization of rational algebraic curves and surfaces, that is to say the computation of the image of a curve...
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Self-intersection of nod(oid)al curves
We classify the self-intersections of a family of curves sharing the abstract properties of the meridian of a nodoid. For the purposes of this paper...
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Counting elliptic curves over the rationals with a 7-isogeny
We count by height the number of elliptic curves over the rationals, both up to isomorphism over the rationals and over an algebraic closure thereof,...
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Spacelike Framed Curves with Lightlike Components and Singularities of Their Evolutes and Focal Surfaces in Minkowski 3-space
In this paper, we define the evolute and focal surface of a spacelike framed curve with lightlike components in Minkowski 3-space. It is a...
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The periodicity of differential-difference polynomials of entire functions
We present some results on the periodicity of an entire function f ( z ) with its differential-difference polynomials. For instance, we obtain that if f n ...
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Difference Equations and Interpolation Problems for Entire Functions Induced by a Square
AbstractWe consider poly-element difference equations with constant coefficients. We seek a solution in the class of functions that are holomorphic...
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Intrinsic Riemannian Metrics on Spaces of Curves: Theory and Computation
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian...
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Permutohedral complexes and rational curves with cyclic action
We define a moduli space of rational curves with finite-order automorphism and weighted orbits, and we prove that the combinatorics of its boundary...
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Application of the Theory of Tetragonal Curves to the Hierarchy of Extended Volterra Lattices
The theory of tetragonal curves is first applied to the study of discrete integrable systems. Based on the discrete Lenard equation, we derive a...
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On Triple Lines and Cubic Curves: The Orchard Problem Revisited
Planar point sets with many triple lines (which contain at least three distinct points of the set) have been studied for 180 years, started with...
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Difference analogues of the second main theorem for holomorphic curves and arbitrary families of hypersurfaces in projective varieties
Our goal in this paper is to establish some difference analogue of second main theorems for holomorphic curves into projective varieties intersecting...
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Transcendental entire solutions for several quadratic binomial and trinomial PDEs with constant coefficients
This article is concerned with the description of the existence of entire solutions of several quadratic binomial and trinomial partial differential...
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Algorithms for Contractibility of Compressed Curves on 3-Manifold Boundaries
In this paper we prove that the problem of deciding contractibility of an arbitrary closed curve on the boundary of a 3-manifold is in NP . We...
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Approximation in the Mean on Rational Curves
In the presence of a positive, compactly supported measure on an affine algebraic curve, we relate the density of polynomials in Lebesgue
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Combinatorial Properties of Self-Overlap** Curves and Interior Boundaries
We study the interplay between the recently defined concept of minimum homotopy area and the classical topic of self-overlap** curves . The latter...
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Entire functions arising from trees
Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function f with only two critical values ±1...