scholarly journals On the classification of rank 2 almost Fano bundles on projective space

2012 ◽  
Vol 12 (2) ◽  
Author(s):  
Kazunori Yasutake
Keyword(s):  
Projective Space ◽  
Rank 2 ◽  
Almost Fano

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals Codimension One Holomorphic Distributions on the Projective Three-space

2018 ◽  
Vol 2020 (23) ◽  
pp. 9011-9074 ◽  
Author(s):  
Omegar Calvo-Andrade ◽  
Maurício Corrêa ◽  
Marcos Jardim
Keyword(s):  
Projective Space ◽  
Moduli Space ◽  
Tangent Bundle ◽  
Projective Variety ◽  
Arbitrary Degree ◽  
Codimension One ◽  
Quot Scheme ◽  
Space Of Distributions ◽  
Three Space

Abstract We study codimension one holomorphic distributions on the projective three-space, analyzing the properties of their singular schemes and tangent sheaves. In particular, we provide a classification of codimension one distributions of degree at most 2 with locally free tangent sheaves and show that codimension one distributions of arbitrary degree with only isolated singularities have stable tangent sheaves. Furthermore, we describe the moduli space of distributions in terms of Grothendieck’s Quot-scheme for the tangent bundle. In certain cases, we show that the moduli space of codimension one distributions on the projective space is an irreducible, nonsingular quasi-projective variety. Finally, we prove that every rational foliation and certain logarithmic foliations have stable tangent sheaves.

scholarly journals On real hypersurfaces in quaternionic projective space with𝒟⊥-recurrent second fundamental tensor

1999 ◽  
Vol 22 (1) ◽  
pp. 109-117
Author(s):  
Young Jin Suh ◽  
Juan De Dios Pérez
Keyword(s):  
Projective Space ◽  
Complete Classification ◽  
Real Hypersurfaces ◽  
Quaternionic Projective Space ◽  
Fundamental Tensor ◽  
Orthogonal Distribution

In this paper, we give a complete classification of real hypersurfaces in a quaternionic projective spaceQPmwith𝒟⊥-recurrent second fundamental tensor under certain condition on the orthogonal distribution𝒟.

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