We study the rank and geometry of the multibody fundamental matrix, a geometric entity characterizing the two-view geometry of dynamic scenes consisting of multiple rigidbody motions. We derive an upper bound on the rank of the multibody fundamental matrix that depends on the number of independent translations. We also derive an algebraic characterization of the SVD of a multibody fundamental m...

Abstract We study the geometry of smooth non-homogeneous horospherical varieties Picard rank one. These have been classified by Pasquier and include well-known odd symplectic Grassmannians. focus our on quantum cohomology, with a view towards Dubrovin’s conjecture. start describing cohomology groups show Chevalley formula for these establish that many Gromov–Witten invariants are enumerative. T...

There are two basic theorems. Let G be a strong parapolar space with these three properties: (1) For each point x and symplecton S, x is collinear to some point of S. (2) The set of points at distance at most two from a point forms a geometric hyperplane. (3) If every symplecton has rank at least three, every maximal singular subspace has finite projective rank. Then G is either D6; 6;A5; 3 or ...

In this paper, we extend work from [M. Vancliff and P. Veerapen, Generalizing the notion of rank to noncommutative quadratic forms, in Noncommutative Birational Geometry, Representations Combinatorics, eds. A. Berenstein V. Retakh, Contemporary Mathematics, Vol. 592 (2013), pp. 241–250], where a rank, called [Formula: see text]-rank, was proposed for forms on two three generators. particular, p...

The core of multiple-view geometry is governed by the fundamental matrix and the trilinear tensor. In this paper we unify both representations by rst deriving the fundamental matrix as a rank-2 trivalent tensor, and secondly by deriving a uniied set of operators that are transparent to the number of views. As a result, we show that the basic building block of the geometry of multiple views is a...