Irreducible components of characteristic varieties
نویسنده
چکیده
We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial di.erential equations de0ned from a suitable 0ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety de0ned from the order 0ltration is involutive. More explicitly, we consider a 0ltration of An induced by any vector (u; v)∈Zn ×Zn such that the associated graded algebra is a commutative polynomial ring. Any 0nitely generated left An-module M has a good 0ltration 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. MSC: 16S32; 13P10; 17B35
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