Article
Exponential growth of rank jumps for A-hypergeometric systems
Author/s | Fernández Fernández, María Cruz |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2013 |
Deposit Date | 2016-06-08 |
Published in |
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Abstract | The dimension of the space of holomorphic solutions at nonsingular
points (also called the holonomic rank) of a A–hypergeometric system
MA(β) is known to be bounded above by 22d vol(A) [SST00], where d is the
rank of ... The dimension of the space of holomorphic solutions at nonsingular points (also called the holonomic rank) of a A–hypergeometric system MA(β) is known to be bounded above by 22d vol(A) [SST00], where d is the rank of the matrix A and vol(A) is its normalized volume. This bound was thought to be very vast because it is exponential on d. Indeed, all the examples we have found in the literature verify that rank(MA(β)) < 2vol(A). We construct here, in a very elementary way, some families of matrices A(d) ∈ Z d×n and parameter vectors β(d) ∈ C d , d ≥ 2, such that rank(MA(d) (β(d) )) ≥ a dvol(A(d) ) for certain a > 1. |
Project ID. | MTM2010-19336
FQM-5849 FQM333 |
Citation | Fernández Fernández, M.C. (2013). Exponential growth of rank jumps for A-hypergeometric systems. Revista Matemática Iberoamericana, 29 (4), 1397-1404. |
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