Artal Bartolo, EnriqueCarmona Ruber, JorgeCogolludo Agustín, José Ignacio2023-06-202023-06-2020070002-994710.1090/S0002-9947-06-03881-5https://hdl.handle.net/20.500.14352/50721In this paper we construct new invariants of algebraic curves based on (not necessarily generic) braid monodromies. Such invariants are effective in the sense that their computation allows for the study of Zariski pairs of plane curves. Moreover, the Zariski pairs found in this work correspond to curves having conjugate equations in a number field, and hence are not distinguishable by means of computing algebraic coverings. We prove that the embeddings of the curves in the plane are not homeomorphic. We also apply these results to the classification problem of elliptic surfaces.engjournal articlehttp://www.ams.org/journals/tran/2007-359-01/S0002-9947-06-03881-5/S0002-9947-06-03881-5.pdfhttp://www.ams.orgrestricted access512.7Braid monodromyPlane curveGroup representations.Geometria algebraica1201.01 Geometría Algebraica