Monodromy conjecture for Newton non-degenerate hypersurfaces

Authors

Keywords:

monodromy, Bernstein–Sato polynomial, resolution of singularities, plane curves, Newton non-degenerate

Abstract

This work studies the Strong Monodromy Conjecture (SMC) in its topological setting. After introducing the concepts of resolution of singularities, Bernstein–Sato polynomial, and the zeta function, we sketch the results involved in the proof of the SMC for Newton non-degenerate (NND) singularities. This approach requires nonetheless additional hypothesis on the residue numbers, and we construct examples showing that they can’t be dropped, which suggests that new techniques are needed to attack the general case.

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Published

2025-12-04

How to Cite

Baeza Guasch, O. (2025). Monodromy conjecture for Newton non-degenerate hypersurfaces. Reports@SCM, 10(1), 31–42. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/155250

Issue

Vol. 10 No. 1 (2025)

Section

Articles

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