Related papers: Generalised pairs in birational geometry

This is the first in a series of two papers concerned with relative birational geometry of algebraic spaces. In this paper, we study Pr\"ufer spaces and Pr\"ufer pairs of algebraic spaces that generalize spectra of Pr\"ufer rings. As a…

A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.

Extending the work of Freese, we further develop the theory of generalized trigonometric functions. In particular, we study to what extent the notion of polar form for the complex numbers may be generalized to arbitrary associative…

We discuss new problems in universal algebraic geometry and explain them by boolean equations.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

The concept of (p,q)-pair frames is generalized to (l,l^*)-pair frames. Adjoint (conjugate) of a pair frames for dual space of a Banach space is introduced and some conditions for the existence of adjoint (conjugate) of pair frames are…

We introduce many new generalizations of Poisson algebras which can be constructed inside the associative algebra of linear transformations over a vector space.

We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to…

Generalized models provide a framework for the study of evolution equations without specifying all functional forms. The generalized formulation of problems has been shown to facilitate the analytical investigation of local dynamics and has…

We develop a generalised gauge theory in which the role of gauge group is played by a coalgebra and the role of principal bundle by an algebra. The theory provides a unifying point of view which includes quantum group gauge theory,…

We study the theory specialisations in algebraic geometry from a model theoretic viewpoint. In particular we investigate universality and maximality of specialisations in algebraic geometry.

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…

A priori, the set of birational transformations of an algebraic variety is just a group. We survey the possible algebraic structures that we may add to it, using in particular parametrised family of birational transformations.

In this talk I review various notions of generalised global symmetry: higher-form, higher-group, and non-invertible symmetry. All these notions have had profound impact on quantum field theory research in the last decade. I highlight…

We construct and study universal spaces for birational invariants of algebraic varieties over algebraic closures of finite fields.

We review the concept of a graded bundle as a natural generalisation of a vector bundle. Such geometries are particularly nice examples of more general graded manifolds. With hindsight there are many examples of graded bundles that appear…

In this note, our goal is to describe the concept of generalized derivations in the context of BiHom-supertrialgebras. We provide a comprehensive analysis of the properties and applications of these generalized derivations, including their…

The notion of prolongation of an algebraic variety is developed in an abstract setting that generalises the difference and (Hasse) differential contexts. An interpolating map that compares the prolongation spaces with algebraic jet spaces…

This paper considers generalizations of open mappings, closed mappings, pseudo-open mappings, and quotient mappings from topological spaces to generalized topological spaces. Characterizations of these classes of mappings are obtained and…

Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…