The Nash problem for surfaces

DOI10.4007/annals.2012.176.3.11zbMath1264.14049arXiv1102.2212OpenAlexW2119307599MaRDI QIDQ1928622

María Pe Pereira, J. Fernández de Bobadilla de Olazabal

Publication date: 3 January 2013

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1102.2212

zbMATH Keywords

singularitiesresolution of singularitiessurfaceswedgesspace of arcscoinsNash's problem

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Singularities of surfaces or higher-dimensional varieties (14J17)

Related Items (18)

Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR) ⋮ On the configuration of the singular fibers of jet schemes of rational double points ⋮ Deforming spaces of \(m\)-jets of hypersurfaces singularities ⋮ Arcology ⋮ On the generalized Nash problem for smooth germs and adjacencies of curve singularities ⋮ Families of \(m\)-jet spaces and arc spaces ⋮ Normalized Berkovich spaces and surface singularities ⋮ Deformations of arcs and comparison of formal neighborhoods for a curve singularity ⋮ On the Nash problem for terminal threefolds of type cA/r ⋮ Nash problem for surface singularities is a topological problem ⋮ Nash’s work in algebraic geometry ⋮ Jacobian discrepancies and rational singularities ⋮ The embedded Nash problem of birational models of rational triple singularities ⋮ The arc space of the Grassmannian ⋮ Differentials on the arc space ⋮ The Nash problem and its solution: a survey ⋮ Nash blow-ups of jet schemes ⋮ Holomorphic arcs on singularities

Cites Work

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• Some Numerical Criteria for the Nash Problem on Arcs for Surfaces
• Nash problem for stable toric varieties
• Euler characteristic of the Milnor fibre of plane singularities
• Arcs and wedges on sandwiched surface singularities
• Exceptional divisors that are not uniruled belong to the image of the Nash map
• Three-dimensional counter-examples to the Nash problem
• Bijectiveness of the Nash Map for Quasi-Ordinary Hypersurface Singularities
• Singular Points of Complex Hypersurfaces. (AM-61)
• Arcs, valuations and the Nash map

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