000100654 001__ 100654 000100654 005__ 20231127095532.0 000100654 0248_ $$2sideral$$a122228 000100654 0247_ $$2doi$$a10.48550/arXiv.1912.08670 000100654 037__ $$aART-2021-122228 000100654 041__ $$aeng 000100654 100__ $$0(orcid)0000-0002-8276-5116$$aArtal Bartolo, Enrique$$uUniversidad de Zaragoza 000100654 245__ $$aCyclic branched coverings of surfaces with abelian quotient singularities 000100654 260__ $$c2021 000100654 5060_ $$aAccess copy available to the general public$$fUnrestricted 000100654 5203_ $$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 (X̃, C) in terms of a resolution of the ramification locus. Later, in [1] the first author applies 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. 000100654 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-17R$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-76868-C2-2-P 000100654 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000100654 590__ $$a1.059$$b2021 000100654 592__ $$a1.326$$b2021 000100654 594__ $$a2.0$$b2021 000100654 591__ $$aMATHEMATICS$$b141 / 333 = 0.423$$c2021$$dQ2$$eT2 000100654 593__ $$aMathematics (miscellaneous)$$c2021$$dQ1 000100654 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000100654 700__ $$0(orcid)0000-0003-1820-6755$$aCogolludo-Agustín, José Ignacio$$uUniversidad de Zaragoza 000100654 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, Jorge$$uUniversidad de Zaragoza 000100654 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000100654 773__ $$g2 (2021), [27 pp.]$$pIndiana Univ. math. j.$$tINDIANA UNIVERSITY MATHEMATICS JOURNAL$$x0022-2518 000100654 85641 $$uhttps://www.iumj.indiana.edu/IUMJ/Preprints/8768.pdf$$zTexto completo de la revista 000100654 8564_ $$s524186$$uhttps://zaguan.unizar.es/record/100654/files/texto_completo.pdf$$yPreprint 000100654 8564_ $$s2217614$$uhttps://zaguan.unizar.es/record/100654/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000100654 909CO $$ooai:zaguan.unizar.es:100654$$particulos$$pdriver 000100654 951__ $$a2023-11-27-09:47:15 000100654 980__ $$aARTICLE