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arXiv · 1911.07539

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

José Ignacio Cogolludo-Agustín·Tamás László·Jorge Martín-Morales·András Némethi
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Abstract

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 (X,C). 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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José Ignacio Cogolludo-Agustín, Tamás László, Jorge Martín-Morales, András Némethi. 2019-11-18. Delta invariant of curves on rational surfaces I. The analytic approach. https://arxiv.org/abs/1911.07539

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