Kac's question, planar isospectral pairs and involutions in projective space: II. Classification of generalized projective isospectral data

2006 ◽  
Vol 39 (42) ◽  
pp. 13237-13242 ◽  
Author(s):  
Koen Thas
Keyword(s):  
Projective Space

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.

scholarly journals Classification of 3T1R Parallel Manipulators Based on Their Wrench Graph

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Semaan Amine ◽  
Ossama Mokhiamar ◽  
Stéphane Caro
Keyword(s):  
Projective Space ◽  
Parallel Manipulator ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Geometrical Properties ◽  
Cayley Algebra ◽  
Dimensional Projective Space ◽  
Grassmann Cayley Algebra

This paper presents a classification of 3T1R parallel manipulators (PMs) based on the wrench graph. By using the theory of reciprocal screws, the properties of the three-dimensional projective space, the wrench graph, and the superbracket decomposition of Grassmann–Cayley algebra, six typical wrench graphs for 3T1R parallel manipulators are obtained along with their singularity conditions. Furthermore, this paper shows a way in which each of the obtained typical wrench graphs can be used in order to synthesize new 3T1R parallel manipulator architectures with known singularity conditions and with an understanding of their geometrical properties and assembly conditions.

scholarly journals On the equations and classification of toric quiver varieties

2016 ◽  
Vol 146 (2) ◽  
pp. 265-295 ◽  
Author(s):  
Mátyás Domokos ◽  
Dániel Joó
Keyword(s):  
Projective Space ◽  
Moduli Spaces ◽  
Toric Variety ◽  
Projective Variety ◽  
Homogeneous Ideal ◽  
Quiver Representations ◽  
Canonical Embedding ◽  
Quiver Varieties ◽  
Fixed Dimension

Toric quiver varieties (moduli spaces of quiver representations) are studied. Given a quiver and a weight, there is an associated quasi-projective toric variety together with a canonical embedding into projective space. It is shown that for a quiver with no oriented cycles the homogeneous ideal of this embedded projective variety is generated by elements of degree at most 3. In each fixed dimension d up to isomorphism there are only finitely many d-dimensional toric quiver varieties. A procedure for their classification is outlined.

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