2010/06/11 by Rémi Arcadias, Arcadias, Rémi
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Rings and Algebras (math.RA) #math.AC #math.RA
paper · pdf · doi:10.48550/arxiv.1006.2298
24 pages
arxiv created 2010/06/11 · openalex publication_date 2010/06/11 · arxiv updated 2010/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.