000118829 001__ 118829 000118829 005__ 20240731103311.0 000118829 0247_ $$2doi$$a10.1090/conm/778/15660 000118829 0248_ $$2sideral$$a130236 000118829 037__ $$aART-2022-130236 000118829 041__ $$aeng 000118829 100__ $$0(orcid)0000-0003-1820-6755$$aCogolludo-Agustín, José$$uUniversidad de Zaragoza 000118829 245__ $$aLocal invariants of minimal generic curves on rational surfaces 000118829 260__ $$c2022 000118829 5060_ $$aAccess copy available to the general public$$fUnrestricted 000118829 5203_ $$aLet (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'.) 000118829 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E22-20R$$9info:eu-repo/grantAgreement/EC/FP7/615655/EU/New methods and interacions in Singularity Theory and beyond/NMST$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033$$9info:eu-repo/grantAgreement/ES/MINECO/SEV-2017-0718 000118829 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000118829 592__ $$a0.425$$b2022 000118829 593__ $$aMathematics (miscellaneous)$$c2022 000118829 594__ $$a0.9$$b2022 000118829 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000118829 700__ $$aLászló, Tamás 000118829 700__ $$0(orcid)0000-0002-6559-4722$$aMartín-Morales, Jorge$$uUniversidad de Zaragoza 000118829 700__ $$aNémethi, András 000118829 7102_ $$12006$$2440$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Geometría y Topología 000118829 773__ $$g778 (2022), 231-258$$pContemp. math.- Am. Math. Soc.$$tContemporary mathematics - American Mathematical Society$$x0271-4132 000118829 8564_ $$s571666$$uhttps://zaguan.unizar.es/record/118829/files/texto_completo.pdf$$yPostprint 000118829 8564_ $$s1736060$$uhttps://zaguan.unizar.es/record/118829/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000118829 909CO $$ooai:zaguan.unizar.es:118829$$particulos$$pdriver 000118829 951__ $$a2024-07-31-09:39:36 000118829 980__ $$aARTICLE