The monodromy conjecture for a space monomial curve with a plane semigroup

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 every pole of the motivic, or related, Igusa zeta function induces an eigenvalue of monodromy. As the poles of the motivic zeta function associated with such a space monomial curve have been determined in earlier work, it remains to study the eigenvalues of monodromy. After reducing the problem to the curve seen as a Cartier divisor on a generic embedding surface, we construct an embedded Q-resolution of this pair and use an A’Campo formula in terms of this resolution to compute the zeta function of monodromy. Combining all results, we prove the monodromy conjecture for this class of monomial curves

Note on the monodromy conjecture for a space monomial curve with a plane semigroup

Roughly speaking, the monodromy conjecture for a singularity states that every pole of its motivic Igusa zeta function induces an eigenvalue of its monodromy. In this note, we determine both the motivic Igusa zeta function and the eigenvalues of monodromy for a space monomial curve that appears as the special fiber of an equisingular family whose generic fiber is a plane branch. In particular, this yields a proof of the monodromy conjecture for such a curve. En gros, la conjecture de la monodromie pour une singularité dit que chaque pôle de sa fonction zêta d’Igusa motivique induit une valeur propre de sa monodromie. Dans cette note, nous déterminons la fonction zêta d’Igusa motivique ainsi que les valeurs propres de la monodromie pour une courbe d’espace monomiale qui apparaît comme fibre spéciale d’une famille équisingulière dont la fibre générique est une branche plane. En particulier, il en résulte une démonstration de la conjecture de la monodromie pour une telle courb

Igusa's p-adic local zeta function associated to a polynomial mapping and a polynomial integration measure

For p prime, we give an explicit formula for Igusa's local zeta function associated to a polynomial mapping f=(f_1,...,f_t): Q_p^n -> Q_p^t, with f_1,...,f_t in Z_p[x_1,...,x_n], and an integration measure on Z_p^n of the form |g(x)||dx|, with g another polynomial in Z_p[x_1,...,x_n]. We treat the special cases of a single polynomial and a monomial ideal separately. The formula is in terms of Newton polyhedra and will be valid for f and g sufficiently non-degenerated over F_p with respect to their Newton polyhedra. The formula is based on, and is a generalization of results of Denef - Hoornaert, Howald et al., and Veys - Zuniga-Galindo.Comment: 20 pages, 5 figures, 2 table

In situ observation of compressive deformation of an interconnected network of zinc oxide tetrapods

Zinc oxide tetrapods have remarkable functional and mechanical properties with potential applications in different fields including nanoelectronic and optoelectronic sensing, functional composites and coatings, as well as energy harvesting and storage. Based on the 3D shape of these microparticles, they can be assembled into highly porous (up to 98%) macroscopic ceramic framework structures that can be utilized as a versatile template for the fabrication of other multi-scaled foam-like materials. Here we investigated the three-dimensional structure of low density interconnected zinc oxide tetrapod networks by high resolution X-ray computed tomography. In situ observations during mechanical loading show inhomogeneous development of anelastic strain (damage) during compression, and homogeneous elastic recovery on unloading. Individual tetrapods are observed to deform by arm rotation to accommodate strain

The diagnostic value of synovial histopathology in undifferentiated inflammatory arthritis: a prospective study in 154 consecutive patients

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