Local invariants of minimal generic curves on rational surfaces

2020/05/20 by José Agustín, Tamás László, Cogolludo-Agustín, José Ignacio +5
Computer Science · Engineering · Mathematics · #32Sxx #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Polynomial and algebraic computation #Primary. 14B05 #Secondary. 14E15

paper · pdf · doi:10.48550/arxiv.2005.10155

openalex publication_date 2020/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (C,0) be a reduced curve germ in a normal surface singularity (X,0). The main goal is to recover the delta invariant of the abstract curve (C,0) from the topology of the embedding. We give explicit formulae whenever (C,0) is minimal generic and (X,0) is rational (as a continuation of previous works of the authors). Additionally we prove that if (X,0) is a quotient singularity, then the delta invariant of (C,0) only admits the values r-1 or r, where r is the number or irreducible components of (C,0). (r-1 realizes the extremal lower bound, valid only for `ordinary r-tuples'.)

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