Related papers: Calculation of two Belyi pairs
We compute Betti numbers of both the components of the moduli space of rank 2 semi-stable torsion-free sheaves with fixed determinant over a reducible nodal curve with two smooth components intersecting at a node. We also compute the…
In the first part of this paper we prove a conjecture of Hikami on the values of the radial limits of a family of $q$-hypergeometric false theta functions. Hikami conjectured that the radial limits are obtained by evaluating a truncated…
We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions…
An elliptic exceptional Belyi covering is a connected Belyi covering uniquely determined by its ramification scheme or the respective dessin d'enfant when the underlying compact Riemann surface has genus 1. We give our Maple algorithm and…
We exhibit an explicit algorithm to compute three-point branched covers of the complex projective line when the uniformizing triangle group is Euclidean.
We explicitly bound the Faltings height of a curve over Q polynomially in its Belyi degree. Similar bounds are proven for three other Arakelov invariants: the discriminant, Faltings' delta invariant and the self-intersection of the…
We provide a simple method to compute the Betti numbers if the Stanley-Reisner ideal of a simplicial tree and its Alexander dual.
It is known that sometimes a Belyi pair is not defined over its field of moduli. Instead, it is defined over a finite degree extension of its field of moduli, called a field of definition. We show that given a number $m$ there exists a…
We consider the multi-parameter random simplicial complex as a higher dimensional extension of the classical Erd\"os-R\'enyi graph. We investigate appearance of "unusual" topological structures in the complex from the point of view of large…
In this paper, we first establish two new Bailey pairs via finding two generalizations of Euler's pentagonal number theorem. Next, we specificize the Bailey lemmas with these two Bailey pairs. As applications, we finally establish some…
Exceptional Belyi covering is a connected Belyi covering uniquely determined by its ramification scheme or the respective dessin d'enfant. We focus on rational exceptional Belyi coverings of compact Riemann surfaces of genus 0. Well known…
Studying the mirror symmetry of a Calabi-Yau threefold $X$ of the Reye congruence in $\mP^4$, we conjecture that $X$ has a non-trivial Fourier-Mukai partner $Y$. We construct $Y$ as the double cover of a determinantal quintic in $\mP^4$…
The ground state multiplet structure for nuclei over the wide range of mass number $A$ was calculated in $\delta$-approximation and different mass relations for pairing energy was analysed in this work. Correlation between the calculated…
In this paper, we study discrete quasi-copulas associated with imprecise copulas. We focus on discrete imprecise copulas that are in correspondence with the Alternating Sign Matrices and provide some construction techniques of dual pairs.…
In a weakly correlated inhomogeneous plasma an equation of pair correlation function is obtained utilizing the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations. In this article the pair correlation function has been…
We present a method of obtaining a Belyi map on an elliptic curve from that on the Riemann sphere. This is done by writing the former as a radical of the latter, which we call a quadratic correspondence, with the radical determining the…
Chu has recently shown that the Abel lemma on summations by parts can serve as the underlying relation for Bailey's ${}_6\psi_6$ bilateral summation formula. In other words, the Abel lemma spells out the telescoping nature of the…
We offer some partition functions related to ternary quadratic forms, and note on their upper bounds and related properties. We offer these results as an application of a simple method related to conjugate Bailey pairs presented in a prior…
In this paper, dual complex Pell numbers and quaternions are defined. Also, some algebraic properties of dual-complex Pell numbers and quaternions which are connected with dual complex numbers and Pell numbers are investigated. Furthermore,…