doi:10.1090/conm/778/15660engCogolludo-Agustín, JoséLászló, TamásMartín-Morales, JorgeNémethi, AndrásLocal invariants of minimal generic curves on rational surfacesART-2022-130236Let (C, 0) be a reduced curve germ in a normal surface singularity (X, 0). The main goal is to recover the delta invariant [delta](C) of the abstract curve (C, 0) from the topology of the embedding (C, 0) ⊂ (X, 0). We give explicit formulae whenever (C, 0) is minimal generic and (X, 0) is rational (as continuation of [8, 9]). Additionally, in this case, we prove that if (X, 0) is a quotient singularity, then [delta](C) only admits the values r−1 or r, where r is the number or irreducible components of (C, 0). ([delta](C) = r − 1 realizes the extremal lower bound, valid only for 'ordinary r–tuples'.)2022http://zaguan.unizar.es/record/11882910.1090/conm/778/15660http://zaguan.unizar.es/record/118829oai:zaguan.unizar.es:118829info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/EC/FP7/615655/EU/New methods and interacions in Singularity Theory and beyond/NMSTinfo:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033info:eu-repo/grantAgreement/ES/MINECO/SEV-2017-0718Contemporary mathematics - American Mathematical Society 778 (2022), 231-258by-nc-ndhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccess