The thick-thin decomposition and the bilipschitz classification of normal surface singularities

DOI10.1007/s11511-014-0111-8zbMath1303.14016arXiv1105.3327OpenAlexW2080862420MaRDI QIDQ2015962

Anne Pichon, Lev Birbrair, Walter D. Neumann

Publication date: 18 June 2014

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.3327

zbMATH Keywords

normal surface singularitythick-thin decompositionbilipschitz geometrymetrically conical

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) General low-dimensional topology (57M99) Complex surface and hypersurface singularities (32S25) Local complex singularities (32S05)

Related Items (25)

Multiplicity, regularity and blow-spherical equivalence of real analytic sets ⋮ Inner geometry of complex surfaces: a valuative approach ⋮ Lipschitz Normal Embedding Among Superisolated Singularities ⋮ On Lipschitz normally embedded complex surface germs ⋮ The genericity of the infinitesimal Lipschitz condition for hypersurfaces ⋮ Lipschitz geometry of complex curves ⋮ Polar exploration of complex surface germs ⋮ Exceptional rays and bilipschitz geometry of real surface singularities ⋮ Arc spaces, motivic measure and Lipschitz geometry of real algebraic sets ⋮ Lipschitz stratification of complex hypersurfaces in codimension 2 ⋮ Zariski’s dimensionality type of singularities. Case of dimensionality type 2 ⋮ Singularities. Abstracts from the workshop held September 26 -- October 2, 2021 (hybrid meeting) ⋮ Choking horns in Lipschitz geometry of complex algebraic varieties. Appendix by Walter D. Neumann ⋮ A quick trip into local singularities of complex curves and surfaces ⋮ 3-manifolds and links of singularities ⋮ An introduction to Lipschitz geometry of complex singularities ⋮ On Milnor’s fibration theorem and its offspring after 50 years ⋮ A characterization of Lipschitz normally embedded surface singularities ⋮ Pencils and critical loci on normal surfaces ⋮ Lipschitz normal embeddings in the space of matrices ⋮ Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections ⋮ On the growth behaviour of Hironaka quotients ⋮ Lipschitz Geometry Does not Determine Embedded Topological Type ⋮ A topological introduction to Lipschitz geometry of complex singularities ⋮ Tangent Cones of Lipschitz Normally Embedded Sets Are Lipschitz Normally Embedded. Appendix by Anne Pichon and Walter D. Neumann

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(L^ 2\)-cohomology of normal algebraic surfaces. I
• Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen. (On four-dimensional Riemann surfaces of many-valued analytic functions of two complex variables)
• Bi-Lipschitz geometry of weighted homogeneous surface singularities
• The boundary of the Milnor fiber for some non-isolated singularities of complex surfaces
• Bi-Lipschitz geometry of complex surface singularities
• Singularités rationnelles et quotients par les groupes réductifs. (Rational singularities and quotients by reductive groups)
• The \(\mu\)-constant stratum is not smooth
• Lipschitz properties of semi-analytic sets
• Limites d'espaces tangents en géométrie analytique. (Limits of tangent spaces in analytic geometry)
• Résolution de Nash des points doubles rationnels
• Variétés polaires locales et classes de Chern des variétés singulieres
• Plongements dans les variétés feuilletees et classification de feuilletages sans holonomie
• Canonical decompositions of 3-manifolds
• Topological equivalence of complex curves and bi-lipschitz homeomorphisms
• Remarks on the \(L^ 2\)-cohomology of singular algebraic surfaces
• Hilbert modular surfaces
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• On irreducible 3-manifolds which are sufficiently large
• Sandwiched singularities and desingularization of surfaces by normalized Nash transformations
• GEOMETRY OF CRITICAL LOCI
• Neighborhoods of Algebraic Sets
• A Calculus for Plumbing Applied to the Topology of Complex Surface Singularities and Degenerating Complex Curves
• Inner metric geometry of complex algebraic surfaces with isolated singularities
• Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM-110)
• Courbes polaires et topologie des courbes planes
• Lipschitz stratification of subanalytic sets
• The link of {f(x, y) + zn = 0} and Zariski's conjecture
• The link of the germ of a semi-algebraic metric space
• Links and analytic invariants of superisolated singularities
• Tangent spaces and Gromov-Hausdorff limits of subanalytic spaces
• Singular Points of Complex Hypersurfaces. (AM-61)
• Noncobordant foliations of 𝑆³
• Fibrations sur le cercle et surfaces complexes. (Fibrations over the circle and complex surfaces)
• Limits of tangent spaces of a normal surface
• Separating sets, metric tangent cone and applications for complex algebraic germs

This page was built for publication: The thick-thin decomposition and the bilipschitz classification of normal surface singularities