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- Title
On the monodromy conjecture for non-degenerate hypersurfaces.
- Authors
Esterov, Alexander; Lemahieu, Ann; Kiyoshi Takeuchi
- Abstract
The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in arithmetic geometry and singularity theory. Even the weakest of these relations - the Denef-Loeser conjecture on topological zeta functions - is open for surface singularities. We prove it for a wide class of multidimensional singularities that are non-degenerate with respect to their Newton polyhedra, including all such singularities of functions of four variables. A crucial difference from the known case of three variables is the existence of degenerate singularities arbitrarily close to a non-degenerate one. Thus, even aiming at the study of non-degenerate singularities, we have to go beyond this setting. We develop new tools to deal with such multidimensional phenomena, and conjecture how the proof for non-degenerate singularities of arbitrarily many variables might look like.
- Subjects
MONODROMY groups; HYPERSURFACES; ZETA functions; POLYNOMIALS; EIGENVALUES; MATHEMATICAL singularities
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2022, Vol 24, Issue 11, p3873
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1241