Details:
Title  Critical cones of characteristic varieties.  Author(s)  Roberto Boldini  Type  Article in Journal  Abstract  Let $ M$ be a left module over a Weyl algebra in characteristic zero. Given natural weight vectors $ \nu $ and $ \omega $, we show that the characteristic varieties arising from filtrations with weight vector $ \nu +s\omega $ stabilize to a certain variety determined by $ M$, $ \nu $, $ \omega $ as soon as the natural number $ s$ grows beyond a bound which depends only on $ M$ and $ \nu $ but not on $ \omega $.
As a consequence, in the notable case when $ \nu $ is the standard weight vector, these characteristic varieties deform to the critical cone of the $ \omega $characteristic variety of $ M$ as soon as $ s$ grows beyond an invariant of $ M$.
As an application, we give a new, easy, nonhomological proof of a classical result, namely, that the $ \omega $characteristic varieties of $ M$ all have the same Krull dimension.
The set of all $ \omega $characteristic varieties of $ M$ is finite. We provide an upper bound for its cardinality in terms of supports of universal Gröbner bases in the case when $ M$ is cyclic. By the above stability result, we conjecture a second upper bound in terms of total degrees of universal Gröbner bases and of Fibonacci numbers in the case when $ M$ is cyclic over the first Weyl algebra.  ISSN  00029947; 10886850/e 
File 
 URL 
http://www.ams.org/journals/tran/201336501/S000299472012055310/home.html 
Language  English  Journal  Trans. Am. Math. Soc.  Volume  365  Number  1  Pages  143160  Publisher  American Mathematical Society (AMS), Providence, RI  Year  2013  Edition  0  Translation 
No  Refereed 
No 
