  In commutative algebra, E. Miller and B. Sturmfels defined the notion of
multidegree for multigraded modules over a multigraded polynomial ring. We
apply this theory to bifiltered modules over the Weyl algebra D. The
bifiltration is a combination of the standard filtration by the order of
differential operators and of the so-called V-filtration along a coordinate
subvariety of the ambient space defined by M. Kashiwara. The multidegree we
define provides a new invariant for D-modules. We investigate its relation with
the L-characteristic cycles considered by Y. Laurent. We give examples from the
theory of A-hypergeometric systems defined by I. M. Gelfand, M. M. Kapranov and
A. V. Zelevinsky. We consider the V-filtration along the origin. When the toric
projective variety defined from the matrix A is Cohen-Macaulay, we have an
explicit formula for the multidegree of the hypergeometric system.
