110723 20230519145614.0 doi 10.5565/PUBLMAT6522105 sideral 127358 ART-2021-127358 eng Martín Morales, J. Universidad de Zaragoza (orcid)0000-0002-6559-4722 The monodromy conjecture for a space monomial curve with a plane semigroup 2021 Access copy available to the general public Unrestricted 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. info:eu-repo/grantAgreement/ES/DGA/E22-17R info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 1.475 2021 MATHEMATICS 72 / 333 = 0.216 2021 Q1 T1 1.046 2021 Mathematics (miscellaneous) 2021 Q1 2.1 2021 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Veys, W. Vos, L. 2006 440 Universidad de Zaragoza Dpto. Matemáticas Área Geometría y Topología 65, 2 (2021), 529-597 Publ. mat. Publicacions Matematiques 0214-1493 793430 http://zaguan.unizar.es/record/110723/files/texto_completo.pdf Versión publicada 1293465 http://zaguan.unizar.es/record/110723/files/texto_completo.jpg?subformat=icon icon Versión publicada https://mat.uab.cat/pubmat/volums/navegador# Texto completo de la revista oai:zaguan.unizar.es:110723 articulos driver 2023-05-18-16:09:59 ARTICLE