Related papers: A Database of Belyi Maps
We describe our online database of finite extensions of the p-adic numbers, and how it can be used to facilitate local analysis of number fields.
We study a class of algebraic surfaces of degree 3n in the complex projective space with only ordinary double points. They are obtained by using bivariate polynomials with complex coefficients related to the generalized cosine associated to…
It has recently been shown that cryptographic trilinear maps are sufficient for achieving indistinguishability obfuscation. In this paper we develop a method for constructing such maps on the Weil descent (restriction) of abelian varieties…
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
The task of this survey is to present various results on intersection patterns of convex sets. One of main tools for studying intersection patterns is a point of view via simplicial complexes. We recall the definitions of so called…
Given a finite index subgroup $\Gamma$ of ${\rm{PSL}}_2(\Bbb{Z})$, we investigate Belyi functions on the corresponding modular curve $X(\Gamma)$ by introducing two methods for constructing such functions. Numerous examples have been worked…
We provide a classification result on nearly free arrangements of lines in the complex projective plane with nodes and triple points.
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.
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…
We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
In this work we characterize branch data of branched coverings of even degree over the projective plane which are realizable by indecomposable branched coverings.
Let Y be a surface with only finitely many singularities all of which are cusps. A set of cusps on Y is called three-divisible, if there is a cyclic global triple cover of Y branched precisely over these cusps. The aim of this note is to…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
We study plane algebraic curves defined over a field k of arbitrary characteristic as coverings of the the projective line and the problem of enumerating branched coverings of $\mathbb{P}^{1}$ by using combinatorial methods.
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi--Yau threefolds. An efficient way of encoding this…
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…
Given a point $\xi$ on a complex abelian variety $A$, its abelian logarithm can be expressed as a linear combination of the periods of $A$ with real coefficients, the Betti coordinates of $\xi$. When $(A, \xi)$ varies in an algebraic…
A useful technique for analyzing incomplete tables is to model the missing data mechanisms of the variables using log-linear models. In this paper, we use log-linear parametrization and propose estimation methods for arbitrary three-way and…
We continue our computation, using a combinatorial method based on Gronthendieck's dessins d'enfant, of the number of (weak) equivalence classes of surface branched covers matching certain specific branch data. In this note we concentrate…