Local invariants of minimal generic curves on rational surfaces

Cogolludo-Agustín, José (Universidad de Zaragoza) ; László, Tamás ; Martín-Morales, Jorge (Universidad de Zaragoza) ; Némethi, András

Resumen: Let (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'.)

Idioma: Inglés

DOI: 10.1090/conm/778/15660

Año: 2022

Publicado en: Contemporary mathematics - American Mathematical Society 778 (2022), 231-258
ISSN: 0271-4132

Factor impacto CITESCORE: 0.9 - Mathematics (Q4)

Factor impacto SCIMAGO: 0.425 - Mathematics (miscellaneous)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E22-20R
Financiación: info:eu-repo/grantAgreement/EC/FP7/615655/EU/New methods and interacions in Singularity Theory and beyond/NMST
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033
Financiación: info:eu-repo/grantAgreement/ES/MINECO/SEV-2017-0718

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Geometría y Topología (Dpto. Matemáticas)