Around the motivic monodromy conjecture for non-degenerate hypersurfaces

DOI10.1007/S00229-023-01494-3arXiv2208.02566OpenAlexW4381168037WikidataQ123073420 ScholiaQ123073420MaRDI QIDQ6201293

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Publication date: 20 February 2024

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Abstract: We provide a new, geometric proof of the motivic monodromy conjecture for non-degenerate hypersurfaces in dimension $3$, which has been proven previously by the work of Lemahieu--Van Proeyen and Bories--Veys. More generally, given a non-degenerate complex polynomial $f$ in any number of variables and a set $mathbfB$ of $B_1$-facets of the Newton polyhedron of $f$ with consistent base directions, we construct a stack-theoretic embedded desingularization of $f^{-1}(0)$ above the origin, whose set of numerical data excludes any known candidate pole of the motivic zeta function of $f$ at the origin that arises solely from facets in $mathbfB$. We anticipate that the constructions herein might inspire new insights as well as new possibilities towards a solution of the conjecture.

Full work available at URL: https://arxiv.org/abs/2208.02566

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