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Extended Tropical Characteristic Fibers and Slopes of Binomial D-Modules

  • Jen-Chieh Hsiao
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Abstract

For a holonomic D-module, we consider the extended tropicalization of the reduced L-characteristic fiber along the family Ls=F+(s−1)VY. For A-hypergeometric systems, this tropical fiber determines the complete (A,L)-umbrella and hence recovers the classical slopes. We extend this result to holonomic binomial D-modules, for which the tropical jump parameters are exactly the classical slopes at the origin. As an application, a holonomic binomial D-module is regular holonomic if and only if there are no tropical jumps along any coordinate subspace.

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Cite

BibTeXRIS
BibTeX
@misc{hsiao2026extended,
  title = {{Extended Tropical Characteristic Fibers and Slopes of Binomial D-Modules}},
  author = {Jen-Chieh Hsiao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.41587},
  eprint = {2610.41587},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.41587},
}
RIS
TY  - UNPB
TI  - Extended Tropical Characteristic Fibers and Slopes of Binomial D-Modules
AU  - Jen-Chieh Hsiao
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.41587
UR  - https://arxiv.org/abs/2610.41587
AB  - For a holonomic D-module, we consider the extended tropicalization of the reduced L-characteristic fiber along the family L_s=F+(s−1)V_Y. For A-hypergeometric systems, this tropical fiber determines the complete (A,L)-umbrella and hence recovers the classical slopes. We extend this result to holonomic binomial D-modules, for which the tropical jump parameters are exactly the classical slopes at the origin. As an application, a holonomic binomial D-module is regular holonomic if and only if there are no tropical jumps along any coordinate subspace.
ER  -