Critical cones of characteristic varieties

Details Critical cones of characteristic varieties Critical cones of characteristic varieties

2010-08-02

arxiv.org/abs/1008.0292v5

Mathematics

Rings and Algebras

16 pages, 1 figure, updated on 1st June 2011, to appear on Transactions of the American Mathematical Society

Scientific paper

We show that certain characteristic varieties of a finitely generated module over a given Weyl algebra arising from weighted degree filtrations are equal to the critical cone of some other characteristic varieties. This behaviour of the characteristic varieties permits us to introduce a new invariant of the module. As a second consequence we are able to provide an easy and non-homological proof that the characteristic varieties of a module arising from weights in the natural polynomial region of the Weyl algebra all have the same Krull and Gelfand-Kirillov dimension, equal to the Gelfand-Kirillov dimension of the module. Third we give an upper bound for the number of distinct characteristic varieties of a cyclic module in terms of degrees of elements in universal Groebner bases and the above results allow us to conjecture a further upper bound.

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