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Abstract: Suppose $S$ is a closed, oriented surface of genus $g \geq 2$. This paper investigates the geometry of the "homology multicurve complex", $\mathcal{HC}(S,\alpha)$, of $S$; a complex closely ...
Abstract: A proof that the separating curve complex of the closed genus two surface has a quasi-distance formula and is delta hyperbolic using tools of Masur and Schleimer. This answers in the affirma...
Abstract: Using lower bounds for linear forms in elliptic logarithms we determine the integral points of the modular curve associated to the normalizer of a non-split Cartan group of level 11. As an a...
Abstract: Our purpose is to investigate all defined Poincar\'e series associated with multi-index filtrations and value semigroups of curve singularities---not necessarily complex---with regard to the...
Abstract: This paper deals with the study of the behaviour of the value semigroup of a curve singularity define over a global field reduced modulo a maximal ideal. We also define a global zeta functio...
With few exceptions, known explicit solutions of the curve shortening flow (CSE) of a plane curve, can be constructed by classical Lie point symmetry reductions or by functional separation of variable...
The central curve of a linear program is an algebraic curve speci ed by linear and quadratic constraints arising from complementary slackness. It is the union of the various central paths for minimizi...
Given two elliptic curves over a finite field having the same cardinality and endomorphism ring, it is known that the curves admit an isogeny between them, but finding such an isogeny is believed to ...
In this article we extend the computational geometric curve reconstruction approach to curves in Riemannian manifolds.We prove that the minimal spanning tree, given a sufficiently dense sample set of ...
A symplectic bundle over an algebraic curve has a natural invariant sLag determined by the maximal degree of its Lagrangian subbundles. This can be viewed as a generalization of the classical Segre in...
Let G be a semisimple linear algebraic group over the field C, and let C be an irreducible smooth complex projective curve of genus at least three. We compute the Brauer group of the smooth locus of t...
We show that the generalized Giulietti-Korchm´aros curve and the maximal curve with equation x q2 − x = y (qn+1)/(q+1) defined over F q2n, for n  3 odd and q  3, are not Galois subcovers...
Let C be a smooth projective curve defined over a number field k and let C′ be a twist of C. For every isomorphism : C′! C defined over a finite Galois extension L/k, we introduce a rational Artin re...
Let R be a discrete valuation ring with fraction field K and with algebraically closed residue field of positive characteristic p. Let X be a smooth fibered surface over R with geometrically connected...
In this paper we discus the radial extension $w$ of a bi-Lipschitz parameterization $F(e^{it})=f(t)$ of a starlike Jordan curve $\gamma$ w.r. to $0$. We show that, if parameterization is bi-Lipschitz,...

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