000148199 001__ 148199 000148199 005__ 20250130163247.0 000148199 0247_ $$2doi$$a10.1512/iumj.2022.71.8768 000148199 0248_ $$2sideral$$a141673 000148199 037__ $$aART-2022-141673 000148199 041__ $$aeng 000148199 100__ $$0(orcid)0000-0002-8276-5116$$aArtal Bartolo, E.$$uUniversidad de Zaragoza 000148199 245__ $$aCyclic branched coverings of surfaces with Abelian quotient singularities 000148199 260__ $$c2022 000148199 5060_ $$aAccess copy available to the general public$$fUnrestricted 000148199 5203_ $$aIn [9], Esnault-Viehweg developed the theory of cyclic branched coverings X̃ → X of smooth surfaces providing a very explicit formula for the decomposition of H 1 (X̃, C) in terms of a resolution of the ramification locus. Later, in [1] the first author applied this to the particular case of coverings of P² reducing the problem to a combination of global and local conditions on projective curves. In this paper, we extend the above results in three directions: first, the theory is extended to surfaces with abelian quotient singularities; second, the ramification locus can be partially resolved and need not be reduced, and finally, global and local conditions are given to describe the irregularity of cyclic branched coverings of the weighted projective plane. The techniques required for these results are conceptually different and provide simpler proofs for the classical results. For instance, the local contribution comes from certain modules that have the flavor of quasi-adjunction and multiplier ideals on singular surfaces. As an application, a Zariski pair of curves on a singular surface is described. In particular, we prove the existence of two cuspidal curves of degree 12 in the weighted projective plane P²(1,1,3) with the same singularities but non-homeomorphic embeddings. This is shown by proving that the cyclic covers of P²(1,1,3) of order 12 ramified along the curves have different irregularity. In the process, only a partial resolution of singularities is required. 000148199 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/MTM2016-76868-C2-2-P 000148199 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000148199 590__ $$a1.1$$b2022 000148199 591__ $$aMATHEMATICS$$b101 / 329 = 0.307$$c2022$$dQ2$$eT1 000148199 592__ $$a1.223$$b2022 000148199 593__ $$aMathematics (miscellaneous)$$c2022$$dQ1 000148199 594__ $$a1.7$$b2022 000148199 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000148199 700__ $$0(orcid)0000-0003-1820-6755$$aCogolludo-Agustín, J. I.$$uUniversidad de Zaragoza 000148199 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, J.$$uUniversidad de Zaragoza 000148199 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000148199 773__ $$g71, 1 (2022), 213-249$$pIndiana Univ. math. j.$$tINDIANA UNIVERSITY MATHEMATICS JOURNAL$$x0022-2518 000148199 8564_ $$s504082$$uhttps://zaguan.unizar.es/record/148199/files/texto_completo.pdf$$yPostprint 000148199 8564_ $$s2217614$$uhttps://zaguan.unizar.es/record/148199/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000148199 909CO $$ooai:zaguan.unizar.es:148199$$particulos$$pdriver 000148199 951__ $$a2025-01-30-16:31:23 000148199 980__ $$aARTICLE