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Core Coordinates and Negative Support in A-Hypergeometric Systems

  • Mao Nagamine
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Abstract

For a homogeneous A-hypergeometric system, let Kv be the intersection of the negative support family for a fake exponent v, and let Cw be the set of indices of variables that do not occur in any minimal monomial generator of inw(IA). We prove that Kv=nsupp(v)∩ Cw holds for every parameter and every fake exponent if and only if Cone(ACw) meets the interior of Cone(A). We give equivalent criteria using the reduced Gröbner basis and the associated regular triangulation. When the condition fails, we construct an infinite family of fake exponents for which the equality fails.

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Cite

BibTeXRIS
BibTeX
@misc{nagamine2026core,
  title = {{Core Coordinates and Negative Support in A-Hypergeometric Systems}},
  author = {Mao Nagamine},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.04369},
  eprint = {2610.04369},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.04369},
}
RIS
TY  - UNPB
TI  - Core Coordinates and Negative Support in A-Hypergeometric Systems
AU  - Mao Nagamine
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.04369
UR  - https://arxiv.org/abs/2610.04369
AB  - For a homogeneous A-hypergeometric system, let K_v be the intersection of the negative support family for a fake exponent v, and let C_w be the set of indices of variables that do not occur in any minimal monomial generator of in_w(I_A). We prove that K_v=nsupp(v)∩ C_w holds for every parameter and every fake exponent if and only if Cone(A_C_w) meets the interior of Cone(A). We give equivalent criteria using the reduced Gröbner basis and the associated regular triangulation. When the condition fails, we construct an infinite family of fake exponents for which the equality fails.
ER  -