Communications in Contemporary Mathematics ( IF 1.278 ) Pub Date : 2021-06-09 , DOI: 10.1142/s0219199721500528
José Ignacio Cogolludo-Agustín, Tamás László, Jorge Martín-Morales, András Némethi

We prove that if $(C,0)$ is a reduced curve germ on a rational surface singularity $(X,0)$ then its delta invariant can be recovered by a concrete expression associated with the embedded topological type of the pair $C⊂X$. Furthermore, we also identify it with another (a priori) embedded analytic invariant, which is motivated by the theory of adjoint ideals. Finally, we connect our formulae with the local correction term at singular points of the global Riemann–Roch formula, valid for projective normal surfaces, introduced by Blache.

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