Related papers: Secants of Lagrangian Grassmannians

In this paper we discuss the dimensions of the (higher) secant varieties to the Grassmann varieties, embedded via the Plucker embeddings. We use Terracini's Lemma and the duality in the exterior algebra of a finite dimensional vector space…

Restricted secant varieties of Grassmannians are constructed from sums of points corresponding to $k$-planes with the restriction that their intersection has a prescribed dimension. We study dimensions of restricted secant of Grassmannians…

Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the…

We study the geometry of the secant and tangential variety of a cominuscule and minuscule variety, e.g. a Grassmannian or a spinor variety. Using methods inspired by statistics we provide an explicit local isomorphism with a product of an…

We determine normal forms and ranks of tensors of border rank at most three. We present a differential-geometric analysis of limits of secant planes in a more general context. In particular there are at most four types of points on limiting…

For an irreducible projective variety X, we study the family of h-planes contained in the secant variety Sec_k(X), for 0<h<k. These families have an expected dimension and we study varieties for which the expected dimension is not attained;…

In the first part of the thesis, we study a classical invariant of projective varieties, the secant defectivity. The second part is devoted to modern algebraic geometry, we study the birational geometry of blow-ups of Grassmannians at…

Grassmann cactus variety is a common generalisation of Grassmann secant variety and cactus variety. In their definitions one considers the vector spaces of fixed dimension that are contained in the linear span of some finite schemes. We…

We provide a characterization of Symplectic Grassmannians in terms of their Varieties of Minimal Rational Tangents.

We first prove an identity involving symmetric polynomials. This identity leads us into exploring the geometry of Lagrangian Grassmannians. As an insight applications, we obtain a formula for the integral over the Lagrangian Grassmannian of…

We resolve a basic problem on subspace distances that often arises in applications: How can the usual Grassmann distance between equidimensional subspaces be extended to subspaces of different dimensions? We show that a natural solution is…

We investigate the secant dimensions and the identifiablity of flag varieties parametrizing flag of sub vector spaces of a fixed vector space. We give numerical conditions ensuring that secant varieties of flag varieties have the expected…

We study the projective behavior, mainly with respect to osculating spaces and secant varieties, of Lagrangian Grassmannians and Spinor varieties. We prove that these varieties have osculating dimension smaller than expected. Furthermore,…

Lagrangian curves in 4-space entertain intriguing relationships with second order deformation of plane curves under the special affine group and null curves in a 3-dimensional Lorentzian space form. We provide a natural affine symplectic…

We develop a correspondence between the orbits of the group of linear symplectomorphisms of a real finite dimensional symplectic vector space in the complex Lagrangian Grassmannian and the Grassmannians of linear subspaces of the real…

This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between…

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…

In a four-dimensional space, I shall construct all of the conformally invariant scalar-tensor field theories, which are flat space compatible; i.e., well-defined and differentiable when evaluated for a flat metric tensor and constant scalar…

In this paper we study the higher secant varieties of Grassmann varieties in relation to Waring's problem for alternating tensors and to Alexander-Hirschowitz theorem. We show how to identify defective higher secant varieties of…

This article gives an invariant representation of the curvature of a plane wave spacetime in terms of the Schwarzian of a curve in the Lagrangian Grassmannian. It develops a general theory of cross ratios and Schwarzians of curves in what…