2022-11-082022-11-082022-03-06Berkesch, C. y Fernández Fernández, M.C. (2022). On the rank of an A-hypergeometric D-module versus the normalized volume of A. Bulletin of the London Mathematical Society, 54 (1), 182-192. https://doi.org/10.48550/arXiv.1907.08669.0024-60931469-2120https://hdl.handle.net/11441/139117The rank of an A-hypergeometric D-module MA(β), associated with a full rank (d×n)-matrix A and a vector of parameters β∈Cd, is known to be the normalized volume of A, denoted vol(A), when β lies outside the exceptional arrangement E(A), an affine subspace arrangement of codimension at least two. If β∈E(A) is simple, we prove that d−1 is a tight upper bound for the ratio rank(MA(β))/vol(A) for any d≥3. We also prove that the set of parameters β such that this ratio is at least 2 is an affine subspace arrangement of codimension at least 3.application/pdf10 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Algebraic Geometryinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.48550/arXiv.1907.08669