The dimension of the space of holomorphic solutions at nonsingular points (also called the holonomic rank) of an -hypergeometric system is known to be bounded above by , where is the rank of the matrix and is its normalized volume. This bound was thought to be much too large because it is exponential in . Indeed, all the examples we have found in the literature satisfy . We construct here, in a very elementary way, some families of matrices and parameter vectors , , such that for some .
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María-Cruz Fernández-Fernández, Exponential growth of rank jumps for <var>A</var>-hypergeometric systems. Rev. Mat. Iberoam. 29 (2013), no. 4, pp. 1397–1404DOI 10.4171/RMI/761