Related papers: Exercises in the birational geometry of algebraic …

We introduce a variant of the birational symbols group of Kontsevich, Pestun, and the second author, and use this to define birational invariants of algebraic orbifolds.

We construct algebraic surfaces with a large number of type A singularities. Bivariate polynomials presented in previous works for the construction of nodal surfaces and certain families of Belyi polynomials are used. In some cases explicit…

For every fibration $f : X \to B$ with $X$ a compact K\"ahler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.

This is a cornucopia of types of algebras with some of their properties from the operadic point of view.

We introduce a new construction of towers of algebraic curves over finite fields and provide a simple example of an optimal tower.

This is a survey article about Siegel modular varieties over the complex numbers. It is written mostly from the point of view of moduli of abelian varieties, especially surfaces. We cover compactification of Siegel modular varieties;…

We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing…

We provide a generalization of an algebraic linear combination for the trace of certain elliptic modular forms, and through specializing the expression at a suitable pair consisting of an elliptic curve over algebraic number fields and its…

This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1.…

This is a survey work on Lie algebras with ad-invariant metrics. We summarize main features, notions and constructions, in the aim of bringing into consideration the main research on the topic. We also give some list of examples in low…

We study the distribution of algebraic points on curves in abelian varieties over finite fields.

Arithmetic combinatorics is often concerned with the problem of bounding the behaviour of arbitrary finite sets in a group or ring with respect to arithmetic operations such as addition or multiplication. Similarly, combinatorial geometry…

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

A criterion for the existence of a birational embedding into a projective plane with non-collinear Galois points for algebraic curves is presented. A new example of a plane curve with non-collinear Galois points as an application is…

Additive deformations of bialgebras in the sense of J. Wirth, i.e. deformations of the multiplication map fulfilling a certain compatibility condition w.r.t. the coalgebra structure, can be generalized to braided bialgebras. The theorems…

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of…

We show that the action of the special conformal transformations of the usual (undeformed) conformal group is the $q\to 1$ scaling limit of the braided adjoint action or $R$-commutator of $q$-Minkowski space on itself. We also describe the…

An algebraic deformation theory of coalgebra morphisms is constructed.

We present a systematic technique to find explicit solutions of birational maps, provided that these solutions are given in terms of elliptic functions. The two main ingredients are: (i) application of classical addition theorems for…

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…