Related papers: Towards a general theory of unprojection
Following and generalizing unpublished work of Ange, we prove a generalized version of R\'emond's generalized Vojta inequality. This generalization can be applied to arbitrary products of irreducible positive-dimensional projective…
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
In this paper, we propose a generalization of a congruence due to Carlitz.
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
Detecting and exploiting similarities between seemingly distant objects is without doubt an important human ability. This paper develops \textit{from the ground up} an abstract algebraic and qualitative notion of similarity based on the…
We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional…
We give a generalized version of the Freyd conjecture and a way to think about a possible proof. The essential point is to describe an elementary formal reduction of the question that holds in any triangulated category. There are no new…
In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.
We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…
The coordinate projective line over a field is seen as a groupoid with a further `projection' structure. We investigate conversely to what extent such an, abstractly given, groupoid may be coordinatized by a suitable field constructed out…
The aim of this work is to show how we can decompose a module (if decomposable) into an indecomposable module with the help of the minimization process.
This is a survey of select recent results by a number of authors, inspired by the classical configuration theorems of projective geometry.
We prove several generalisations of the ping-pong lemma for negatively curved groups.
A long-standing conjecture is that any transitive finite projective plane is Desarguesian. We make a contribution towards a proof of this conjecture by showing that a group acting transitively on the the points of a…
We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global…
In this notes, we survey the recent developments on theory of generalized quasidisks. Based on the more or less standard techniques used earlier, we also provide some minor improvements on the recorded results. A few nature questions were…
A tentative proposal is demonstrated that there is a natural strategy to get rid of unphysical (UV) infinities in QFTs if one adopts the modern standard point of view that a fundamental theory that is complete and well-defined in all…
The goal of this note is to show how recent results on the theory of quasi-stationary distributions allow to deduce effortlessly general criteria for the geometric convergence of normalized unbounded semigroups.