On the generalized Nash problem for smooth germs and adjacencies of curve singularities
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2017
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Elsevier
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Fernández De Bobadilla, Javier, et al. «On the Generalized Nash Problem for Smooth Germs and Adjacencies of Curve Singularities». Advances in Mathematics, vol. 320, noviembre de 2017, pp. 1269-317. https://doi.org/10.1016/j.aim.2017.09.035.
Abstract
In this paper we explore the generalized Nash problem for arcs on a germ of smooth surface: given two prime divisors above its special point, to determine whether the arc space of one of them is included in the arc space of the other one. We prove that this problem is combinatorial and we explore its relation with several notions of adjacency of plane curve singularities.