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The monodromy conjecture for high order poles, and norms of residue antiderivatives
Abstract
We prove the strong local monodromy conjecture for poles of order at least n−1 of the naive motivic zeta-function for a complex polynomial of n variables. Moreover, for every such pole s, we construct an explicit homology exp(2πi s)-eigencycle in a neighborhood of any given 1-dimensional exceptional stratum contributing the pole. The proof combines topological techniques developed by the author with a fact of birational geometry discovered by AI.
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BibTeX
@misc{esterov2026monodromy,
title = {{The monodromy conjecture for high order poles, and norms of residue antiderivatives}},
author = {Alexander Esterov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22111},
eprint = {2610.22111},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22111},
}
RIS
TY - UNPB
TI - The monodromy conjecture for high order poles, and norms of residue antiderivatives
AU - Alexander Esterov
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22111
UR - https://arxiv.org/abs/2610.22111
AB - We prove the strong local monodromy conjecture for poles of order at least n−1 of the naive motivic zeta-function for a complex polynomial of n variables. Moreover, for every such pole s, we construct an explicit homology exp(2πi s)-eigencycle in a neighborhood of any given 1-dimensional exceptional stratum contributing the pole. The proof combines topological techniques developed by the author with a fact of birational geometry discovered by AI.
ER -