The Nash problem and its solution: a survey

DOI10.5427/jsing.2015.13mzbMath1327.14021OpenAlexW2325940771MaRDI QIDQ5246758

Mark Spivakovsky, Camille Plénat

Publication date: 22 April 2015

Published in: Journal of Singularities (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c5deb727cb6291aa97fae141b1b7ef3755a7ded2

zbMATH Keywords

space of arcsNash problemNash map

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Modifications; resolution of singularities (complex-analytic aspects) (32S45) Complex surface and hypersurface singularities (32S25)

Related Items (3)

Arcology ⋮ Nash’s work in algebraic geometry ⋮ The embedded Nash problem of birational models of rational triple singularities

Cites Work

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• Nash problem for surface singularities is a topological problem
• A solution to the Nash problem on arcs for a family of quasi-rational hypersurfaces
• The local Nash problem on arc families of singularities
• The Nash problem on arc families of singularities
• The arc space of a toric variety
• Arc structure of singularities
• The Nash problem for surfaces
• Essential divisors, essential components of singular toric varieties
• A family of quai-rational hypersurfaces with bijective Nash map
• Jacobian discrepancies and rational singularities
• Some Numerical Criteria for the Nash Problem on Arcs for Surfaces
• Families of smooth curves on surface singularities and wedges
• Courbes Tracees sur un Germe D'Hypersurface
• Equivalence of the Nash conjecture for primitive and sandwiched 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

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