Mathematics – Algebraic Geometry
Scientific paper
2004-06-18
Mathematics
Algebraic Geometry
Scientific paper
We analyze the behavior of the holonomic rank in families of holonomic systems over complex algebraic varieties by providing homological criteria for rank-jumps in this general setting. Then we investigate rank-jump behavior for hypergeometric systems H_A(\beta) arising from a d x n integer matrix A and a parameter \beta \in \CC^d. To do so we introduce an Euler-Koszul functor for hypergeometric families over \CC^d, whose homology generalizes the notion of a hypergeometric system, and we prove a homology isomorphism with our general homological construction above. We show that a parameter \beta is rank-jumping for H_A(\beta) if and only if \beta lies in the Zariski closure of the set of \ZZ^d-graded degrees \alpha where the local cohomology \bigoplus_{i
Matusevich Laura Felicia
Miller Ezra
Walther Uli
No associations
LandOfFree
Homological Methods for Hypergeometric Families 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 Homological Methods for Hypergeometric Families, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homological Methods for Hypergeometric Families will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-490998