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arXiv · 1206.1889

Local invariants on quotient singularities and a genus formula for weighted plane curves

Jose Ignacio Cogolludo-Agustin·Jorge Martin-Morales·Jorge Ortigas-Galindo
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Abstract

In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. 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.

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Jose Ignacio Cogolludo-Agustin, Jorge Martin-Morales, Jorge Ortigas-Galindo. 2012-06-08. Local invariants on quotient singularities and a genus formula for weighted plane curves. https://arxiv.org/abs/1206.1889

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