A remarkable subset of poles of the motivic zeta function

TL;DR

This paper identifies a special subset of poles of the motivic zeta function linked to log resolutions and contact loci, revealing new challenges in proving the monodromy conjecture.

Contribution

It introduces a combinatorially defined subset of motivic zeta function poles with an intrinsic geometric interpretation, highlighting a novel difficulty in the monodromy conjecture.

Findings

Subset of poles determined by log resolution

Intrinsic interpretation via contact loci

Uncovers new difficulty in monodromy conjecture

Abstract

For any polynomial f with complex coefficients we find a remarkable subset of poles of the motivic zeta function. It is combinatorially determined by any log resolution and it admits an intrinsic interpretation in terms of contact loci of f. This uncovers a new, unexpected difficulty with proving the monodromy conjecture.