Abstract
The rank of an (Formula presented.) -hypergeometric (Formula presented.) -module (Formula presented.), associated with a full-rank (Formula presented.) -matrix (Formula presented.) and a vector of parameters (Formula presented.), is known to be the normalized volume of (Formula presented.), denoted (Formula presented.), when (Formula presented.) lies outside the exceptional arrangement (Formula presented.), an affine subspace arrangement of codimension at least two. If (Formula presented.) is simple, we prove that (Formula presented.) is a tight upper bound for the ratio (Formula presented.) for any (Formula presented.). We also prove that the set of parameters (Formula presented.) such that this ratio is at least two is an affine subspace arrangement of codimension at least three.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 182-192 |
| Number of pages | 11 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 54 |
| Issue number | 1 |
| DOIs | |
| State | Published - Feb 2022 |
Bibliographical note
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