Sylvester–Gallai for Arrangements of Subspaces

Sylvester-Gallai for Arrangements of Subspaces

In this work we study arrangements of k-dimensional subspaces V1, . . . , Vn ⊂ C. Our main result shows that, if every pair Va, Vb of subspaces is contained in a dependent triple (a triple Va, Vb, Vc contained in a 2k-dimensional space), then the entire arrangement must be contained in a subspace whose dimension depends only on k (and not on n). The theorem holds under the assumption that Va ∩ ...

0 Local cohomology , arrangements of subspaces and monomial ideals

If k is the field of complex numbers (or, more generally, a field of characteristic zero), the module H i I(R) is known to have a module structure over the Weyl algebra An(k), and one can therefore consider its characteristic cycle, denoted CC(H i I(R)) in this paper (see e.g. [2, I.1.8.5]). On the other hand, the arrangement X defines a partially ordered set P (X) whose elements correspond to ...

Frameness bound for frame of subspaces

In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.

A Long Exact Sequence in Cohomology for Deleted and Restricted Subspaces Arrangements

The notions of deleted and restricted arrangements have been very useful in the study of arrangements of hyperplanes. Let A be an arrangement of hyperplanes and x ∈ A. The deleted and restricted arrangements A and A allows us to compute recursively the Poincaré polynomials of the complement space M(A) with the following formula : Poin(M(A), t) = Poin(M(A′), t) + tPoin(M(A′′), t). In this paper,...

Group Actions on Arrangements of Linear Subspaces and Applications to Connguration Spaces