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The varieties of bifocal Grassmann tensors
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a...
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Grassmann and Stiefel Varieties over Composition Algebras
This monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical...
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A Grassmann manifold handbook: basic geometry and computational aspects
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in...
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Compact Torus Action on the Complex Grassmann Manifolds
We survey recent achievements in the theory of the canonical action of the compact torus on the complex Grassmann manifolds. The fundamental problem...
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Stiefel, Grassmann Manifolds and Generalizations
In this chapter we investigate and prove some properties of the classical manifolds of Stiefel, Grassmann and flag manifolds.
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Basic 𝕋-Spaces in the Relatively Free Grassmann Algebra Without Unity
In this paper, we consider the 𝕋-space structure of the relatively free Grassmann algebra 𝔽 (3) without unity over an infinite field of prime and...
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Relative Bott–Samelson Varieties
We prove that, defined with respect to versal flags, the product of two relative Bott–Samelson varieties over a flag bundle is a resolution of...
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Basic 𝕋-Spaces in the Relatively Free Grassmann Algebra Without Unity
In this paper, we consider the 𝕋-space structure of the relatively free Grassmann algebra 𝔽 (3) without unity over an infinite field of prime and...
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From Grassmann complements to Hodge-duality
Hodge duality is a central concept of 20th century algebraic and analytic geometry and plays a non-negligible role also in recent mathematical...
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More Classical Matrix Varieties
In this chapter we generalize Stiefel, Grassmann and flag manifolds, defined in Chap. 3 , to what we call...
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Restricted secant varieties of Grassmannians
Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to k -planes with the restriction that their...
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Distinguishing secant from cactus varieties
Cactus varieties are a generalization of secant varieties. They are defined using linear spans of arbitrary finite schemes of bounded length, while...
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A rim-hook rule for quiver flag varieties
The Abelian/non-Abelian correspondence for cohomology (Martin in Symplectic quotients by a nonabelian group and by its maximal torus.
ar**v:math/0001002... 
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Algebraic Generalizations of Matrix Varieties
We use Chaps. 1 and 2 to define and extend results of Chaps....
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Problems and related results in algebraic vision and multiview geometry
This article is a survey of results in algebraic vision and multiview geometry. The starting point is the study of projective algebraic varieties...
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Applications of homogeneous fiber bundles to the Schubert varieties
This article explores the relationship between Schubert varieties and equivariant embeddings, using the framework of homogeneous fiber bundles over...
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Identifiability and singular locus of secant varieties to Grassmannians
Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Grassmannians...
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The Critical Space for Orthogonally Invariant Varieties
Let q be a nondegenerate quadratic form on V . Let X ⊂ V be invariant for the action of a Lie group G contained in S O ( V , q ). For any f ∈ V consider the...
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Grassmann Inequalities and Extremal Varieties in \({\mathbb {P}}\left( {{ \bigwedge ^p}{\mathbb {R}^n}} \right) \)
In continuation of the work in Leventides and Petroulakis (Adv Appl Clifford Algebras 27:1503–1515, 2016), Leventides et al. (J Optim Theory Appl...
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Construction and characterisation of the varieties of the third row of the Freudenthal–Tits magic square
We characterise the varieties appearing in the third row of the Freudenthal–Tits magic square over an arbitrary field, in both the split and...