Delta invariant of curves on rational surfaces I. An analytic approach

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