Related papers: The monodromy conjecture for zeta functions associ…

The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the…

This article investigates the monodromy conjecture for a space monomial curve that appears as the special fiber of an equisingular family of curves with a plane branch as generic fiber. Roughly speaking, the monodromy conjecture states that…

The holomorphy conjecture predicts that the local Igusa zeta function associated to a hypersurface and a character is holomorphic on $\mathbb{C}$ whenever the order of the character does not divide the order of any eigenvalue of the local…

Motivic and topological zeta functions are singularity invariants, mainly associated to a function $f$ and a top differential form $\omega$ on a smooth variety. When $\omega$ is the standard form $dx_1\wedge \dots \wedge dx_n$ on affine…

To an ideal in $\mathbb{C}[x,y]$ one can associate a topological zeta function. This is an extension of the topological zeta function associated to one polynomial. But in this case we use a principalization of the ideal instead of an…

This paper presents a proof of the monodromy conjecture for determinantal varieties. Our strategy centers on an in-depth analysis of monodromy zeta functions, leveraging a generalized A'Campo formula, an examination of multiple contact…

In this article we consider surfaces that are general with respect to a 3- dimensional toric idealistic cluster. In particular, this means that blowing up a toric constellation provides an embedded resolution of singularities for these…

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2\pi i c) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture…

For a complex polynomial or analytic function f, one has been studying intensively its so-called local zeta functions or complex powers; these are integrals of |f|^{2s}w considered as functions in s, where the w are differential forms with…

The holomorphy conjecture states roughly that Igusa's zeta function associated to a hypersurface and a character is holomorphic on $\mathbb{C}$ whenever the order of the character does not divide the order of any eigenvalue of the local…

We give a proof the monodromy conjecture relating the poles of motivic zeta functions with roots of b-functions for isolated quasihomogeneous hypersurfaces, and more generally for semi-quasihomogeneous hypersurfaces. We also give a strange…

We prove the local motivic monodromy conjecture for singularities that are nondegenerate with respect to a simplicial Newton polyhedron. It follows that all poles of the local topological zeta functions of such singularities correspond to…

The aim of the article is an extension of the Monodromy Conjecture of Denef and Loeser in dimension two, incorporating zeta functions with differential forms and targeting all monodromy eigenvalues, and also considering singular ambient…

These notes give a basic introduction to the theory of $p$-adic and motivic zeta functions, motivic integration, and the monodromy conjecture.

In 2011 Lemahieu and Van Proeyen proved the Monodromy Conjecture for the local topological zeta function of a non-degenerated surface singularity. We start from their work and obtain the same result for Igusa's p-adic and the motivic zeta…

By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas…

A notion of Milnor fibration for meromorphic functions and the corresponding concepts of monodromy and monodromy zeta function have been introduced in [GZLM1]. In this article we define the topological zeta function for meromorphic germs…

We prove several results on monodromies associated to Macdonald integrals, that were used in our previous work on the finite field analogue of a conjecture of Macdonald. We also give a new proof of our formula expressing recursively the…

For a generic (polynomial) one-parameter deformation of a complete intersection, there is defined its monodromy zeta-function. We provide explicit formulae for this zeta-function in terms of the corresponding Newton polyhedra in the case…

The main objective of this paper is to prove the monodromy conjecture for the local Igusa zeta function of a quasi-ordinary polynomial of arbitrary dimension defined over a number field. In order to do it, we compute the local Denef-Loeser…