scholarly journals Geometrical Methods in Goursat Categories

2021 ◽  
pp. 397-426
Author(s):  
Brice Réné Amougou Mbarga
Keyword(s):  
Equivalence Relations ◽  
Geometric Methods ◽  
Modular Varieties

The main aim of the paper is to show that the Little Desarguesian Theorem, the Escher Cube, Closure Lemma 1 and 3, hold in any regular Mal'tsev categories. We prove that Mal'tsev categories may be characterized through variations of the Little Desarguesian Theorem, the Escher Cube, Closure Lemma 1 and 3, that is classically expressed in terms of four congruences R, S1, S2 and T, and characterizes congruence modular varieties. The proof of this result in a varietal context may be obtained exclusively through the Little Desarguesian Theorem, the Escher Cube, Closure Lemma 1 and 3. This was shown by H.P. Gumm in Geometric Methods in Congruence Modular Algebras. We prove that for any 2n+1-permutable category $\mathcal{E}$, the category Equiv$(\mathcal{E})$ of equivalence relations in $\mathcal{E}$ is also a 2n+1-permutable category.

Weakly precomplete equivalence relations in the Ershov hierarchy

2019 ◽  
Vol 58 (3) ◽  
pp. 297-319
Author(s):  
N. A. Bazhenov ◽  
B. S. Kalmurzaev
Keyword(s):  
Equivalence Relations ◽  
Ershov Hierarchy

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

2017 ◽  
Author(s):  
Claire Voisin
Keyword(s):  
Recent Work ◽  
Chow Groups ◽  
Ring Structure ◽  
Complete Intersections ◽  
Algebraic Varieties ◽  
Chow Ring ◽  
Hodge Structures ◽  
Chow Rings ◽  
Geometric Methods ◽  
The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

Equivalence relations among inequalities for some relative operator entropies

Positivity ◽  
2020 ◽  
Vol 24 (5) ◽  
pp. 1503-1518
Author(s):  
Ismail Nikoufar ◽  
Maryam Fazlolahi
Keyword(s):  
Equivalence Relations

Fundamental relations and identities of fuzzy hyperalgebras

2021 ◽  
pp. 1-10
Author(s):  
Narjes Firouzkouhi ◽  
Abbas Amini ◽  
Chun Cheng ◽  
Mehdi Soleymani ◽  
Bijan Davvaz
Keyword(s):  
Universal Algebra ◽  
Equivalence Relation ◽  
Polynomial Function ◽  
Equivalence Relations ◽  
Fundamental Relation ◽  
Term Function ◽  
Biological Phenomena ◽  
Definition Of

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

scholarly journals Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lara B. Anderson ◽  
James Gray ◽  
Magdalena Larfors ◽  
Matthew Magill ◽  
Robin Schneider
Keyword(s):  
Vector Bundles ◽  
Geometric Approach ◽  
Low Energy ◽  
Geometric Features ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Alternative Derivation ◽  
Yukawa Couplings ◽  
Geometric Methods ◽  
Higher Dimensional

Abstract Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

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