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arXiv · 2610.18395

Remarks on the monodromy conjecture for symmetric determinantal hypersurfaces

Renjie Lyu·Xiping Zhang
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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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Renjie Lyu, Xiping Zhang. 2026-10-13. Remarks on the monodromy conjecture for symmetric determinantal hypersurfaces. https://arxiv.org/abs/2610.18395

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