Publications [#243927] of Ezra Miller

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Peer-reviewed journal articles published

1. with Matusevich, LF; Miller, E. "Combinatorics of rank jumps in simplicial hypergeometric systems." Proceedings of the American Mathematical Society 134.5 (May, 2006): 1375-1381. [MR2006j:33016], [math.AC/0402071], [doi]
   (last updated on 2024/08/27)

   Abstract:
   Let A be an integer d × n matrix, and assume that the convex hull conv(A) of its columns is a simplex of dimension d - 1 not containing the origin. It is known that the semigroup ring ℂ[Ndbl;A] is Cohen-Macaulay if and only if the rank of the GKZ hypergeometric system H A(β) equals the normalized volume of conv(A) for all complex parameters β ε ℂ d (Saito, 2002). Our refinement here shows that H A(β) has rank strictly larger than the volume of conv(A) if and only if β lies in the Zariski closure (in ℂ d) of all Zdbl; d-graded degrees where the local cohomology ⊕ i