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PreprintarXiv licencearXiv

Remarks on the monodromy conjecture for symmetric determinantal hypersurfaces

  • Renjie Lyu
  • Xiping Zhang
Open at sourcePDFDOICite

Abstract

We compute the local and global Denef--Loeser topological zeta functions of the determinant on the space of symmetric matrices. It verifies the strong monodromy conjecture of the symmetric determinant function. The computation relates to the geometry of complete quadrics and wonderful embeddings.

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Cite

BibTeXRIS
BibTeX
@misc{lyu2026remarks,
  title = {{Remarks on the monodromy conjecture for symmetric determinantal hypersurfaces}},
  author = {Renjie Lyu and Xiping Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18395},
  eprint = {2610.18395},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18395},
}
RIS
TY  - UNPB
TI  - Remarks on the monodromy conjecture for symmetric determinantal hypersurfaces
AU  - Renjie Lyu
AU  - Xiping Zhang
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.18395
UR  - https://arxiv.org/abs/2610.18395
AB  - We compute the local and global Denef--Loeser topological zeta functions of the determinant on the space of symmetric matrices. It verifies the strong monodromy conjecture of the symmetric determinant function. The computation relates to the geometry of complete quadrics and wonderful embeddings.
ER  -