The delta invariant of curves on rational surfaces II: Poincar\'e series and topological aspects

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

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arXiv · 2003.07110

The delta invariant of curves on rational surfaces II: Poincar\'e series and topological aspects

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

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Abstract

In this article we study abstract and embedded invariants of reduced curve germs via topological techniques. One of the most important numerical analytic invariants of an abstract curve is its delta invariant. Our primary goal is to develop delta invariant formulae for curves embedded in rational singularities in terms of embedded data. The topological machinery not only produces formulae, but it also creates deep connections with the theory of (analytical and topological) multivariable Poincar\'e series.

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José Ignacio Cogolludo-Agustín, Tamás László, Jorge Martín-Morales, András Némethi. 2020-03-16. The delta invariant of curves on rational surfaces II: Poincar\'e series and topological aspects. https://arxiv.org/abs/2003.07110

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