The monodromy conjecture for a space monomial curve with a plane semigroup
Martin-Morales, Jorge (Centro Universitario de la Defensa)
Veys, Willem (KU Leuven. Departement Wiskunde)
Vos, Lena (KU Leuven. Departement Wiskunde)

Date:	2021
Abstract:	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:	The first author is partially supported by MTM2016-76868-C2-2-P from the Departamento de Industria e Innovación del Gobierno de Aragón and Fondo Social Europeo E22 17R Grupo Consolidado Algebra y Geometría, and by FQM-333 from Junta de Andalucía. The second author is partially supported by the Research Foundation - Flanders (FWO) project G.0792.18N. The third author is supported by a PhD Fellowship of the Research Foundation - Flanders (no. 71587).
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Monodromy conjecture ; Zeta functions ; Resolution of singularities ; Weighted blow-ups ; Curve singularities
Published in:	Publicacions matemàtiques, Vol. 65 Núm. 2 (2021) , p. 529-597 (Articles) , ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/390241
DOI: 10.5565/PUBLMAT6522105

69 p, 774.8 KB

The record appears in these collections:
Articles > Published articles > Publicacions matemàtiques
Articles > Research articles