scholarly journals Set-theoretic defining equations of the tangential variety of the Segre variety

2011 ◽  
Vol 215 (6) ◽  
pp. 1516-1527 ◽  
Author(s):  
Luke Oeding
Keyword(s):  
Segre Variety

The geometry and topology of entanglement: Conifold, Segre variety, and Hopf fibration

2006 ◽  
Vol 6 (4&5) ◽  
pp. 400-409
Author(s):  
H. Heydari
Keyword(s):  
Higher Order ◽  
Segre Variety ◽  
Hopf Fibration ◽  
And Topology ◽  
Qubit States

We establish relations between conifold, Segre variety, Hopf fibration, and separable sets of pure two-qubit states. Moreover, we investigate the geometry and topology of separable sets of pure multi-qubit states based on the complex multi-projective Segre variety and higher order Hopf fibration. We show that the Segre variety and Hopf fibration give a unified geometrical and topological picture of multi-qubit states. We also construct entanglement monotones for multi-qubit states.

scholarly journals The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 314 ◽  
Author(s):  
Alessandra Bernardi ◽  
Enrico Carlini ◽  
Maria Catalisano ◽  
Alessandro Gimigliano ◽  
Alessandro Oneto
Keyword(s):  
Algebraic Geometry ◽  
Projective Variety ◽  
Tensor Decomposition ◽  
Tensor Rank ◽  
Segre Variety ◽  
Secant Varieties ◽  
Open Problems ◽  
Veronese Variety ◽  
Strong Motivation

We consider here the problem, which is quite classical in Algebraic geometry, of studying the secant varieties of a projective variety X. The case we concentrate on is when X is a Veronese variety, a Grassmannian or a Segre variety. Not only these varieties are among the ones that have been most classically studied, but a strong motivation in taking them into consideration is the fact that they parameterize, respectively, symmetric, skew-symmetric and general tensors, which are decomposable, and their secant varieties give a stratification of tensors via tensor rank. We collect here most of the known results and the open problems on this fascinating subject.

scholarly journals Maximum scattered linear sets of pseudoregulus type and the Segre variety $\mathcal{S}_{n,n}$

2013 ◽  
Vol 39 (4) ◽  
pp. 807-831 ◽  
Author(s):  
G. Lunardon ◽  
G. Marino ◽  
O. Polverino ◽  
R. Trombetti
Keyword(s):  
Segre Variety ◽  
Linear Sets

scholarly journals Cap partitions of the Segre variety S1,3

2002 ◽  
Vol 255 (1-3) ◽  
pp. 7-12
Author(s):  
R.D. Baker ◽  
A. Bonisoli ◽  
A. Cossidente ◽  
G.L. Ebert
Keyword(s):  
Segre Variety

scholarly journals Twisted cubic curves in the Segre variety

2015 ◽  
Vol 353 (12) ◽  
pp. 1123-1127 ◽  
Author(s):  
Kiryong Chung ◽  
Wanseok Lee
Keyword(s):  
Segre Variety ◽  
Cubic Curves ◽  
Twisted Cubic

scholarly journals Geometry of Higher-Order Markov Chains

2012 ◽  
Vol 3 (1) ◽  
Author(s):  
Bernd Sturmfels
Keyword(s):  
Markov Chains ◽  
Prime Ideal ◽  
Linear Space ◽  
Projective Variety ◽  
Likelihood Function ◽  
Distribution Model ◽  
Segre Variety ◽  
Linear Forms ◽  
Transition Distribution ◽  
Binary Case

We determine an explicit Grobner basis, consisting of linear forms and determinantalquadrics, for the prime ideal of Raftery's mixture transition distribution model for Markov chains.When the states are binary, the corresponding projective variety is a linear space, the model itselfconsists of two simplices in a cross-polytope, and the likelihood function typically has two localmaxima. In the general non-binary case, the model corresponds to a cone over a Segre variety.

scholarly journals Base Point Freeness, Uniqueness of Decompositions and Double Points for Veronese and Segre Varieties

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2344
Author(s):  
Edoardo Ballico
Keyword(s):  
Projective Plane ◽  
Linear Systems ◽  
Tangent Vector ◽  
Base Point ◽  
Uniqueness Problem ◽  
Segre Variety ◽  
Double Points ◽  
Segre Varieties ◽  
Tangent Vectors

We prove a base point freeness result for linear systems of forms vanishing at general double points of the projective plane. For tensors we study the uniqueness problem for the representation of a tensor as a sum of terms corresponding to points and tangent vectors of the Segre variety associated with the format of the tensor. We give complete results for unions of one point and one tangent vector.

The cubic Segre variety in PG(5, 2)

2008 ◽  
Vol 51 (2) ◽  
pp. 141-156 ◽  
Author(s):  
Ron Shaw ◽  
Neil A. Gordon
Keyword(s):  
Segre Variety

Prime ideals and postulation formulae

1948 ◽  
Vol 44 (1) ◽  
pp. 43-49 ◽  
Author(s):  
L. S. Goddard
Keyword(s):  
Prime Ideal ◽  
Complete Intersection ◽  
Pezzo Surface ◽  
Prime Ideals ◽  
Segre Variety ◽  
Quadric Surface ◽  
Irreducible Curve ◽  
Del Pezzo Surface ◽  
Veronese Surface ◽  
Del Pezzo

1. In this paper we find explicitly the base for the prime ideal associated with any irreducible Vd−1 on a Segre variety, or a Veronesean variety, Vd. This work extends that of an earlier paper (1) in which the base was found when the Vd−1 is a complete intersection of Vd with one primal. As particular examples we can write down the base for any irreducible curve on a quadric surface, a Veronese surface or a Del Pezzo surface. We also show how the base for any prime ideal changes under a Veronesean transformation.

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