Irreducible components of characteristic varieties

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial differential equations defined from a suitable filtration of the Weyl algebra A(n). This generalizes an important consequence of the fact that a characteristic variety defined from the order filtration is involutive. More explicitly, we consider a filtration of A, induced by any vector (u, v) is an element of Z(n) x Z(n) such that the associated graded algebra is a commutative polynomial ring. Any finitely generated left A(n)-module M has a good filtration with respect to (u,v) and this gives rise to a characteristic variety Ch((u, v))(M) which depends only on (u,v) and M. When (u, v) = (0, 1), the characteristic variety is involutive and this implies that its irreducible components have dimension at least n. In general, the characteristic variety may fail to be involutive, but we are still able to prove that each irreducible component of Ch((u, v))(M) has dimension at least n. (C) 2001 Published by Elsevier Science B.V.