We obtain the symplectic group Sp(V ) as the universal completion of an amalgam of low rank subgroups akin to Levi components. We let Sp(V ) act flag-transitively on the geometry of maximal rank subspaces of V . We show that this geometry and its rank ≥ 3 residues are simply connected with few exceptions. The main exceptional residue is described in some detail. The amalgamation result is then ...

The notion of beingMoishezon to a set of types, a natural strengthening of internality motivated by complex geometry, is introduced. Under the hypothesis of Pillay’s [6] canonical base property, and using results of Chatzidakis [2], it is shown that if a stationary type of finite U -rank at least two is almost internal to a nonmodular minimal type and admits a diagonal section, then it is Moish...

We prove that a binary geometry of rank n {n > 2) not containing M(Ky and F-, (respectively, M(K5) and C10) as a minor has at most 3/i 3 (respectively, 4« 5) points. Here, M(K5) is the cycle geometry of the complete graph on five vertices, F-, the Fano plane, and C10 a certain rank 4 ten-point geometry containing the dual Fano plane F* as a minor. Our technique is elementary and uses the notion...

In arithmetic geometry, cohomology groups are not vector spaces as in classical algebraic geometry but rather euclidean lattices. As a consequence, to understand these groups we need to evaluate not only their rank, but also their successive minima, which are fundamental invariants in the geometry of numbers. The goal of this article is to perform this task for line bundles on projective curves...

In this paper we demonstrate the possibility of using rank conditions as a guiding principle to unify the study of multiple view geometry, for either static or dynamical scenes. A way of classifying rank conditions is proposed for various cases that may arise in the more general context where multiple views of a dynamical scene are considered. We demonstrate by concrete examples why a few doctr...

With the notable exceptions of two cases — that tensors of order 2, namely, matrices, always have best approximations of arbitrary low ranks and that tensors of any order always have the best rank-one approximation, it is known that high-order tensors may fail to have best low rank approximations. When the condition of orthogonality is imposed, even under the modest assumption that only one set...