Mathematics – Algebraic Geometry
Scientific paper
1999-12-08
Journal of Pure and Applied Algebra 165 (2001) 291-306
Mathematics
Algebraic Geometry
20 pages
Scientific paper
10.1016/S0022-4049(01)00109-8
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 $A_{n}(k)$. 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 $A_{n}(k)$ induced by any vector $(u,v) \in {\mathbb Z}^{n}\times {\mathbb Z}^{n}$ such that the associated graded algebra is the commutative polynomial ring in $2n$ indeterminates. The order filtration is the special case $(u,v) = (0,1)$. Any finitely generated left $A_{n}(k)$-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 $n$.
No associations
LandOfFree
Irreducible components of characteristic varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Irreducible components of characteristic varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Irreducible components of characteristic varieties will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-23914