Related papers: On computing Belyi maps
We present the geometry lying behind counting twin prime polynomials in $\mathbb{F}_q[T]$ in general. We compute cohomology and explicitly count points by means of a twisted Lefschetz trace formula applied to these parametrizing varieties…
We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…
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…
We initiate a classification of complex polynomials f of degree d having the top Betti number of the general fibre close to the maximum. We find a range in which the polynomial must have isolated singularities and another range where it may…
We define a period map for classical Campedelli surfaces, using a covering trick as in the case of Enriques surfaces: the period map is shown to come from a family of Enriques surfaces, obtained as quotients of the Campedelli surface by an…
In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily…
We give a method for the computation of integral points on a hyperelliptic curve of odd degree over the rationals whose genus equals the Mordell-Weil rank of its Jacobian. Our approach consists of a combination of the $p$-adic approximation…
We give explicit parametric equations for all irreducible plane projective sextic curves which have at most double points and whose total Milnor number is maximal (is equal to 19). In each case we find a parametrization over a number field…
A type of iterative orthogonally accumulated projection methods for solving linear system of equations are proposed in this paper. This type of methods are applications of accumulated projection(AP) technique proposed recently by authors.…
By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as modular functions, together with the elliptic modular function, we generate the modular function fields of level $N\geq3$.…
We study the geometry of a birational map between an intersection of a web of quadrics in seven-dimensional complex projective space that contains a plane and the double octic branched along the discriminant of the web.
After defining convex near-polygons, a formula enumerating the number of triangulations of such configurations is derived in terms of edge-polynomials. The paper describes also a transfer-matrix approach for computing quantities related to…
We examine in detail the stable reduction of Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup of order p^n. If G is further assumed to be…
We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when…
The complement of plane algebraic curves are well studied from topological and algebro-geometric viewpoints. In this paper, we will describe the explicit handle decompositions and the Kirby diagrams for the complement of plane algebraic…
Allcock and Freitag recently showed that the moduli space of marked cubic surfaces is a subvariety of a nine dimensional projective space which is defined by cubic equations. They used the theory of automorphic forms on ball quotients to…
In this paper, we explicitly compute two kinds of algebraic Belyi functions on Bring's curve. One is related to a congruence subgroup of ${\rm SL}_2(\mathbb{Z})$ and the other is related to a congruence subgroup of the triangle group…
Riemann's Existence Theorem gives the following bijections: (1) Isomorphism classes of Belyi maps of degree $d$. (2) Equivalence classes of generating systems of degree $d$. (3) Isomorphism classes of dessins d'enfants with $d$ edges. In…
A divide-and-conquer algorithm for computing the Betti numbers of finite $T_0$-spaces is presented. It extensively uses the Mayer-Vietoris sequence for open coverings. In the end, the computational costs for a parallelisation of this method…
We give a generalization of the method of "Elliptic Curve Chabauty" to higher genus curves and their Jacobians. This method can sometimes be used in conjunction with covering techniques and a modified version of the Mordell-Weil sieve to…