Related papers: Secants of Lagrangian Grassmannians

The variety of consistent "gauging" deformations of supergravity theories in four dimensions depends on the choice of Lagrangian formulation. One important goal is to get the most general deformations without making hidden assumptions.…

We use a description based on differential forms to systematically explore the space of scalar-tensor theories of gravity. Within this formalism, we propose a basis for the scalar sector at the lowest order in derivatives of the field and…

We study linear series on a general curve of genus g, whose images are exceptional with respect to their secant planes. Each such exceptional secant plane is algebraically encoded by an included linear series, whose number of base points…

Graded Lagrangian formalism in terms of a Grassmann-graded variational bicomplex on graded manifolds is developed in a very general setting. This formalism provides the comprehensive description of reducible degenerate Lagrangian systems,…

We give an explicit combinatorial description of the multiplicity as well as the Hilbert function of the tangent cone at any point on a Schubert variety in the symplectic Grassmannian.

We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduce a number of techniques built on different geometric…

The geometry of a Lagrangian mechanical system is determined by its associated evolution semispray. We uniquely determine this semispray using the symplectic structure and the energy of the Lagrange space and the external force field. We…

A $k$-polar Grassmannian is the geometry having as pointset the set of all $k$-dimensional subspaces of a vector space $V$ which are totally isotropic for a given non-degenerate bilinear form $\mu$ defined on $V.$ Hence it can be regarded…

We give an explicit grobner basis for the ideal of the tangent cone at any T-fixed point of a Richardson variety in the Symplectic Grassmannian, thus generalizing a result of Ghorpade and Raghavan.

In this paper, we investigate tropical secant varieties of ordinary linear spaces. These correspond to the log-limit sets of ordinary toric varieties; we show that their interesting parts are combinatorially isomorphic to a certain natural…

In this paper we deal with symplectic Lie algebras. All symplectic structures are determined for dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described…

We construct the Lagrangian formulation of massive higher spin on-shell (1,0) supermultiplets in three dimensional anti-de Sitter space. The construction is based on description of the massive three dimensional fields in terms of frame-like…

This article gives a classification, up to symplectic equivalence, of singular Lagrangian foliations given by a completely integrable system of a 4-dimensional symplectic manifold, in a full neighbourhood of a singular leaf of focus-focus…

The usual prescription for constructing gauge-invariant Lagrangian is generalized to the case where a Lagrangian contains second derivatives of fields as well as first derivatives. Symmetric tensor fields in addition to the usual vector…

Given a fibration of a symplectic manifold by lagrangian tori, we show that each symplectic vector field splits into two parts : the first is Hamiltonian and the second is symplectic and preserves the fibration. We then show an application…

We obtain a combinatorial expression for the coefficients of the boundary map of real isotropic and odd orthogonal Grassmannians providing a natural generalization of the formulas already obtained for Lagrangian and maximal isotropic…

This paper explores the structure of bi-Lagrangian Grassmanians for pencils of $2$-forms on real or complex vector spaces. We reduce the analysis to the pencils whose Jordan-Kronecker Canonical Form consists of Jordan blocks with the same…

We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a \textit{geometrically compatible} decomposition for any…

We determine the invariants characterizing the $Sp(n)$-orbits in the real Grassmannian $Gr^\R(2k,4n)$ of the $2k$-dimensional complex and $\Sigma$-complex subspaces of a $4n$-dimensional Hermitian quaternionic vector space. A…

A wonderful compactification of an orbit under the action of a semi-simple and simply connected group is a smooth projective variety containing the orbit as a dense open subset, and where the added boundary divisor is simple normal…