Related papers: Real intersection theory (II)
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
We introduce the notion of Lebesgue currents. They are a special type of currents involving Lebesgue measure. We apply it to define the intersection of singular cycles, which provides the foundation to the real intersection theory.
In this paper we survey several intersection and non-intersection phenomena appearing in the realm of symplectic topology. We discuss their implications and finally outline some new relations of the subject to algebraic geometry.
This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them.
We continue our discussion from part I.
We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…
From the method of realization of bialgebras developped in a preceding paper, we obtain the Duality Theorem and apply it to the study of the ideal of relations for each realized bialgebra. This is detailed in the english version of the…
This is the second of two papers establishing structural properties of ${\cal R}_2$.
We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann's theorem to the complex case by proving that complex…
The exposition has been significantly altered, hopefully improved.
This second part of the paper strengthens the descent theory described in the first part to rational maps, arbitrary base fields, and dynamics given by correspondences. We obtain in particular a decomposition of any difference field…
For suitable subgroups of a finitely generated group, we define the intersection number of one subgroup with another subgroup and show that this number is symmetric. We also give an interpretation of this number.
We discuss various phenomena of tangency in projective and convex geometry.
We derive some equalities for relations on the algebra A, under the assumption that every subalgebra of A $\times$ A is congruence modular.
This is a survey of the theory of real trees and their applications.
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras by several ways.
This is a survey on appearances of reflection groups, real and complex, in algebraic geometry. We also include a brief introduction into the theory of reflection groups.
This paper continues the development of the theory of finite localities that was begun in "Finite Localities I". The emphasis in this Part 2.
This is an expository paper on the subject of the title. It assumes basic scheme theory, commutative and homological algebra.
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…