intersection semilattice of a subspace arrangement
Let be a finite subspace arrangement in a finite-dimensional vector space . The of is the subspace arrangement defined by taking the closure (http://planetmath.org/ClosureAxioms) of under intersections. More formally, let
Order (http://planetmath.org/Poset) the elements of by reverse inclusion, and give it the structure of a join-semilattice by defining for all , in . Moreover, the elements of are naturally graded by codimension. If happens to be a central arrangement, its intersection semilattice is in fact a lattice, with the meet operation defined by , where is the subspace of spanned by .
|Title||intersection semilattice of a subspace arrangement|
|Date of creation||2013-03-22 15:47:58|
|Last modified on||2013-03-22 15:47:58|
|Last modified by||CWoo (3771)|