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Pré-Publication, Document De Travail Année : 2022

On the monodromy conjecture for non-degenerate hypersurfaces

Résumé

Recently the second author and Van Proeyen proved the monodromy conjecture on topological zeta functions for all non-degenerate surface singularities. In this paper, we obtain some higher-dimensional analogues of their results. First we study configurations of B 1-pyramid facets which produce fake poles. Secondly, we introduce fully supermodular functions which are useful to find eigenvalues of mon-odromies. Finally, we obtain a result which would be useful to treat the monodromy conjecture for non-degenerate hypersurfaces whose Newton polyhedron is not convenient. In particular, we prove the conjecture for non-degenerate hypersurface singularities in C 4 under some additional assumptions.
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Dates et versions

hal-01279910 , version 1 (27-02-2016)
hal-01279910 , version 2 (13-03-2022)

Identifiants

  • HAL Id : hal-01279910 , version 2

Citer

Alexander Esterov, Ann Lemahieu, Kiyoshi Takeuchi. On the monodromy conjecture for non-degenerate hypersurfaces. 2022. ⟨hal-01279910v2⟩
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