scholarly journals Chow groups and pseudoffective cones of complexity-one T-varieties

2021 ◽  
Author(s):  
Bernt Ivar Utstøl Nødland
Keyword(s):  
Chow Groups ◽  
Generators And Relations ◽  
Combinatorial Data

AbstractWe show that the pseudoeffective cone of k-cycles on a complete complexity-one T-variety is rational polyhedral for any k, generated by classes of T-invariant subvarieties. When X is also rational, we give a presentation of the Chow groups of X in terms of generators and relations, coming from the combinatorial data defining X as a T-variety.

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.

scholarly journals Quiver origami: discrete gauging and folding

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Antoine Bourget ◽  
Amihay Hanany ◽  
Dominik Miketa
Keyword(s):  
Gauge Theories ◽  
Generators And Relations

Abstract We study two types of discrete operations on Coulomb branches of 3d$$ \mathcal{N} $$ N = 4 quiver gauge theories using both abelianisation and the monopole formula. We generalise previous work on discrete quotients of Coulomb branches and introduce novel wreathed quiver theories. We further study quiver folding which produces Coulomb branches of non-simply laced quivers. Our methods explicitly describe Coulomb branches in terms of generators and relations including mass deformations.

scholarly journals On the first Steenrod square for Chow groups

2013 ◽  
Vol 135 (1) ◽  
pp. 53-63 ◽  
Author(s):  
Olivier Haution
Keyword(s):  
Chow Groups ◽  
Steenrod Square

scholarly journals REGULAR FUNCTIONS ON THE SHILOV BOUNDARY

2005 ◽  
Vol 04 (06) ◽  
pp. 613-629 ◽  
Author(s):  
OLGA BERSHTEIN
Keyword(s):  
Symmetric Domain ◽  
Principal Series ◽  
Bounded Symmetric Domain ◽  
Bounded Symmetric Domains ◽  
Shilov Boundary ◽  
Generators And Relations ◽  
Regular Functions ◽  
Degenerate Principal Series

In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.

On multiplicative systems defined by generators and relations

1953 ◽  
Vol 49 (4) ◽  
pp. 579-589 ◽  
Author(s):  
Trevor Evans
Keyword(s):  
Automorphism Group ◽  
Finite Number ◽  
Cyclic Group ◽  
Complete Information ◽  
Isomorphism Problem ◽  
Infinite Cyclic Group ◽  
Generators And Relations ◽  
Decision Method ◽  
Multiplicative Systems ◽  
Finitely Related

The techniques developed in (9) are used here to study the properties of multiplicative systems generated by one element (monogenie systems). The results are of two kinds. First, we obtain fairly complete information about the automorphisms and endo-morphisms of free and finitely related loops. The automorphism group of the free monogenie loop is the infinite cyclic group, each automorphism being obtained by mapping the generator on one of its repeated inverses. A monogenie loop with a finite, non-empty set of relations has only a finite number of endomorphisms. These are obtained by mapping the generator on some of the components, or their repeated inverses, occurring in the relations. We use the same methods to solve the isomorphism problem for monogenie loops, i.e. we give a method for determining whether two finitely related monogenie loops are isomorphic. The decision method consists essentially of constructing all homomorphisms between two given finitely related monogenie loops.

LORENTZ COVARIANCE FOR THE QUANTUM ALGEBRA OF OBSERVABLES: NAMBU–GOTO STRINGS IN 3 + 1 DIMENSIONS

2002 ◽  
Vol 17 (17) ◽  
pp. 2331-2349 ◽  
Author(s):  
GERRIT HANDRICH
Keyword(s):  
Rest Frame ◽  
Poisson Algebra ◽  
Quantum Algebra ◽  
Substantial Part ◽  
Quantum Case ◽  
Generators And Relations ◽  
Defining Relations ◽  
Algebra Of Observables ◽  
The One ◽  
The Relationship

To postulate correspondence for the observables only is a promising approach to a fully satisfying quantization of the Nambu–Goto string. The relationship between the Poisson algebra of observables and the corresponding quantum algebra is established in the language of generators and relations. A very valuable tool is the transformation to the string's rest frame, since a substantial part of the relations are solved. It is the aim of this paper to clarify the relationship between the fully covariant and the rest frame description. Both in the classical and in the quantum case, an efficient method for recovering the covariant algebra from the one in the rest frame is described. Restrictions on the quantum defining relations are obtained, which are not taken into account when one postulates correspondence for the rest frame algebra. For the part of the algebra studied up to now in explicit computations, these further restrictions alone determine the quantum algebra uniquely — in full consistency with the further restrictions found in the rest frame.

scholarly journals The center of the extended Haagerup subfactor has 22 simple objects

2017 ◽  
Vol 28 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Scott Morrison ◽  
Kevin Walker
Keyword(s):  
Fusion Category ◽  
Dimension Function ◽  
Fusion Ring ◽  
Fusion Categories ◽  
Modular Data ◽  
Grothendieck Rings ◽  
Combinatorial Data

We explain a technique for discovering the number of simple objects in [Formula: see text], the center of a fusion category [Formula: see text], as well as the combinatorial data of the induction and restriction functors at the level of Grothendieck rings. The only input is the fusion ring [Formula: see text] and the dimension function [Formula: see text]. In particular, we apply this to deduce that the center of the extended Haagerup subfactor has 22 simple objects, along with their decompositions as objects in either of the fusion categories associated to the subfactor. This information has been used subsequently in [T. Gannon and S. Morrison, Modular data for the extended Haagerup subfactor (2016), arXiv:1606.07165 .] to compute the full modular data. This is the published version of arXiv:1404.3955 .

Sign in / Sign up

Export Citation Format

Share Document