Invariants of four subspaces

Invariants of four subspaces

© Annales de l’institut Fourier, 1998, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...

Configurations of Linear Subspaces and Rational Invariants

We construct a birational equivalence between certain quotients of s-tuples of equidimensional linear subspaces of Cn and some quotients of products of square matrices modulo diagonal conjugations. In particular, we prove the rationality of the quotient space of s-tuples of linear 2-planes in Cn modulo the diagonal GLn(C)-action . Furthermore, we compute generators of the field of the rational ...

Extended Echelon Form and Four Subspaces

Associated with any matrix, there are four fundamental subspaces: the column space, row space, (right) null space, and left null space. We describe a single computation that makes readily apparent bases for all four of these subspaces. Proofs of these results rely only on matrix algebra, not properties of dimension. A corollary is the equality of column rank and row rank. Bringing a matrix to r...

Open Gromov–Witten invariants in dimension four

Given a closed orientable Lagrangian surface L in a closed symplectic four-manifold (X,ω) together with a relative homology class d ∈ H2(X,L;Z) with vanishing boundary in H1(L;Z), we prove that the algebraic number of J-holomorphic discs with boundary on L, homologous to d and passing through the adequate number of points neither depends on the choice of the points nor on the generic choice of ...

Comment on frame's of subspaces