scholarly journals PROJECTIVE THREEFOLDS WITH HOLOMORPHIC CONFORMAL STRUCTURE

2005 ◽  
Vol 16 (06) ◽  
pp. 595-607 ◽  
Author(s):  
PRISKA JAHNKE ◽  
IVO RADLOFF
Keyword(s):  
Tangent Bundle ◽  
Complete Classification ◽  
Conformal Structure ◽  
Complete List ◽  
Projective Threefolds ◽  
Symmetric Square

The authors give a complete classification of projective threefolds admitting a holomorphic conformal structure. A corollary is the complete list of projective threefolds, whose tangent bundle is a symmetric square.

scholarly journals A Complete Classification of 3-dimensional Quadratic AS-regular Algebras of Type EC

2020 ◽  
pp. 1-19
Author(s):  
Masaki Matsuno
Keyword(s):  
Algebraic Geometry ◽  
Complete Classification ◽  
Complete List ◽  
Graded Algebra ◽  
Regular Algebra ◽  
3 Dimensional ◽  
Noncommutative Algebraic Geometry ◽  
Regular Algebras ◽  
Point Scheme

Abstract Classification of AS-regular algebras is one of the main interests in noncommutative algebraic geometry. We say that a $3$ -dimensional quadratic AS-regular algebra is of Type EC if its point scheme is an elliptic curve in $\mathbb {P}^{2}$ . In this paper, we give a complete list of geometric pairs and a complete list of twisted superpotentials corresponding to such algebras. As an application, we show that there are only two exceptions up to isomorphism among all $3$ -dimensional quadratic AS-regular algebras that cannot be written as a twist of a Calabi–Yau AS-regular algebra by a graded algebra automorphism.

Integrability of Dispersionless Hirota-Type Equations and the Symplectic Monge–Ampère Property

2020 ◽  
Author(s):  
E V Ferapontov ◽  
B Kruglikov ◽  
V Novikov
Keyword(s):  
Type Equation ◽  
Lax Pair ◽  
Complete Classification ◽  
Conformal Structure ◽  
Characteristic Variety ◽  
Self Duality ◽  
Symmetry Properties ◽  
Monge Ampere ◽  
Involutive System

Abstract We prove that integrability of a dispersionless Hirota-type equation implies the symplectic Monge–Ampère property in any dimension $\geq 4$. In 4D, this yields a complete classification of integrable dispersionless partial differential equations (PDEs) of Hirota type through a list of heavenly type equations arising in self-dual gravity. As a by-product of our approach, we derive an involutive system of relations characterizing symplectic Monge–Ampère equations in any dimension. Moreover, we demonstrate that in 4D the requirement of integrability is equivalent to self-duality of the conformal structure defined by the characteristic variety of the equation on every solution, which is in turn equivalent to the existence of a dispersionless Lax pair. We also give a criterion of linearizability of a Hirota-type equation via flatness of the corresponding conformal structure and study symmetry properties of integrable equations.

scholarly journals Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jerzy Kowalski-Glikman ◽  
Jerzy Lukierski ◽  
Tomasz Trześniewski
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Complete Classification ◽  
Complete List ◽  
Drinfeld Double ◽  
Lorentzian Signature ◽  
Quantum Deformations ◽  
Chern Simons

Abstract Following the recently obtained complete classification of quantum-deformed $$ \mathfrak{o} $$ o (4), $$ \mathfrak{o} $$ o (1, 3) and $$ \mathfrak{o} $$ o (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail.

scholarly journals The Geometry of Tangent Bundles: Canonical Vector Fields

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Tongzhu Li ◽  
Demeter Krupka
Keyword(s):  
Vector Field ◽  
Linear Combination ◽  
Tangent Bundle ◽  
Vector Fields ◽  
Complete Classification ◽  
Constant Coefficients ◽  
Vertical Lift ◽  
Tangent Bundles ◽  
Canonical Vector

A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift), the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle.

scholarly journals The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices

2016 ◽  
Vol 72 (6) ◽  
pp. 673-683 ◽  
Author(s):  
Mathieu Dutour Sikirić ◽  
Alexey Garber ◽  
Achill Schürmann ◽  
Clara Waldmann
Keyword(s):  
Mass Formula ◽  
Complete Classification ◽  
Complete List ◽  
Computer Assisted ◽  
Voronoi Polyhedra ◽  
Full Classification ◽  
Topological Mass

This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

scholarly journals Nil-clean quadratic elements

2017 ◽  
Vol 16 (10) ◽  
pp. 1750197 ◽  
Author(s):  
Janez Šter
Keyword(s):  
Complete Classification ◽  
Strong Condition ◽  
Clean Rings

We provide a strong condition holding for nil-clean quadratic elements in any ring. In particular, our result implies that every nil-clean involution in a ring is unipotent. As a consequence, we give a complete classification of weakly nil-clean rings introduced recently in [Breaz, Danchev and Zhou, Rings in which every element is either a sum or a difference of a nilpotent and an idempotent, J. Algebra Appl. 15 (2016) 1650148, doi: 10.1142/S0219498816501486].

Ricci inheritance collineations in Bianchi type II spacetime

2016 ◽  
Vol 31 (17) ◽  
pp. 1650102 ◽  
Author(s):  
Tahir Hussain ◽  
Sumaira Saleem Akhtar ◽  
Ashfaque H. Bokhari ◽  
Suhail Khan
Keyword(s):  
Lie Algebra ◽  
Ricci Tensor ◽  
Bianchi Type ◽  
Complete Classification ◽  
Type Ii

In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.

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