We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called \emph{translated} components of the characteristic varieties, and shows that the zero-dimensional components are indeed torsion. The main result is used to derive further obstructions for a group to be the fundamental group of a quasi-projective manifold.Comment: 33 pages, no figures. General rearrangement and proof of Proposition 4.2 is expande

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In this paper we extend the concept of Milnor fiber and Milnor number to curve germs on surface quotient singularities. A generalization of the local δ-invariant is defined and described in terms of a Q-resolution of the curve singularity. In particular, when applied to the classical case (the ambient space is a smooth surface) one obtains a formula for the classical δ-invariant in terms of a Q-resolution, which simplifies considerably effective computations. All these tools will finally allow for an explicit description of the genus formula of a curve defined on a weighted projective plane in terms of its degree and the local type of its singularities.

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.

This paper deals with the invariant R X called the RR-correction term, which appears in the Riemann Roch and Numerical Adjunction Formulas for normal surface singularities. Typically, R X = δ top X − δ an X decomposes as difference of topological and analytical local invariants of its singularities. The invariant δ top X is well understood and depends only on the dual graph of a good resolution. The purpose of this paper is to give a new interpretation for δ an X , which in the case of cyclic quotient singularities can be explicitly computed via generic divisors.We also include two types of applications: one is related to the McKay decomposition of reflexive modules in terms of special reflexive modules in the context of the McKay correspondence. The other application answers two questions posed by Blache [5] on the asymptotic behavior of the invariant R X of the pluricanonical divisor.