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A codimension formula for intrinsic perturbation of A-hypergeometric series

  • Ryunosuke Nakano
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Abstract

We study the canonical formal solution space of a homogeneous A-hypergeometric system in a generic direction. We present as a finite-dimensional cokernel the quotient of that space by the span of the series obtained by intrinsic perturbation, taken over all exponents occurring in that space and all ordered negative support families, and we compute the codimension of that span. We show that the presentation and the codimension transfer to the holomorphic solutions on a common nonsingular domain. We apply these results, for every integer q≥ 1, to a homogeneous A-hypergeometric system of lattice rank 2 with 5q columns. We show that the canonical formal solution space of this system has dimension 12q2 and that the span of the series obtained by intrinsic perturbation has codimension exactly ⌈ 3q2/4⌉ in that space.

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Cite

BibTeXRIS
BibTeX
@misc{nakano2026codimension,
  title = {{A codimension formula for intrinsic perturbation of $A$-hypergeometric series}},
  author = {Ryunosuke Nakano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.22414},
  eprint = {2609.22414},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22414},
}
RIS
TY  - UNPB
TI  - A codimension formula for intrinsic perturbation of A-hypergeometric series
AU  - Ryunosuke Nakano
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.22414
UR  - https://arxiv.org/abs/2609.22414
AB  - We study the canonical formal solution space of a homogeneous A-hypergeometric system in a generic direction. We present as a finite-dimensional cokernel the quotient of that space by the span of the series obtained by intrinsic perturbation, taken over all exponents occurring in that space and all ordered negative support families, and we compute the codimension of that span. We show that the presentation and the codimension transfer to the holomorphic solutions on a common nonsingular domain. We apply these results, for every integer q≥ 1, to a homogeneous A-hypergeometric system of lattice rank 2 with 5q columns. We show that the canonical formal solution space of this system has dimension 12q^2 and that the span of the series obtained by intrinsic perturbation has codimension exactly ⌈ 3q^2/4⌉ in that space.
ER  -