000110723 001__ 110723 000110723 005__ 20230519145614.0 000110723 0247_ $$2doi$$a10.5565/PUBLMAT6522105 000110723 0248_ $$2sideral$$a127358 000110723 037__ $$aART-2021-127358 000110723 041__ $$aeng 000110723 100__ $$0(orcid)0000-0002-6559-4722$$aMartín Morales, J.$$uUniversidad de Zaragoza 000110723 245__ $$aThe monodromy conjecture for a space monomial curve with a plane semigroup 000110723 260__ $$c2021 000110723 5060_ $$aAccess copy available to the general public$$fUnrestricted 000110723 5203_ $$aThis 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. 000110723 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-17R$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P 000110723 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000110723 590__ $$a1.475$$b2021 000110723 592__ $$a1.046$$b2021 000110723 594__ $$a2.1$$b2021 000110723 591__ $$aMATHEMATICS$$b72 / 333 = 0.216$$c2021$$dQ1$$eT1 000110723 593__ $$aMathematics (miscellaneous)$$c2021$$dQ1 000110723 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000110723 700__ $$aVeys, W. 000110723 700__ $$aVos, L. 000110723 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000110723 773__ $$g65, 2 (2021), 529-597$$pPubl. mat.$$tPublicacions Matematiques$$x0214-1493 000110723 85641 $$uhttps://mat.uab.cat/pubmat/volums/navegador#$$zTexto completo de la revista 000110723 8564_ $$s793430$$uhttps://zaguan.unizar.es/record/110723/files/texto_completo.pdf$$yVersión publicada 000110723 8564_ $$s1293465$$uhttps://zaguan.unizar.es/record/110723/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000110723 909CO $$ooai:zaguan.unizar.es:110723$$particulos$$pdriver 000110723 951__ $$a2023-05-18-16:09:59 000110723 980__ $$aARTICLE