Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR)

DOI10.1007/978-3-030-95760-5_3zbMath1506.14010OpenAlexW4285221181MaRDI QIDQ5050030

J. Fernández de Bobadilla de Olazabal

Publication date: 15 November 2022

Published in: Handbook of Geometry and Topology of Singularities III (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-95760-5_3

zbMATH Keywords

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Equisingularity (topological and analytic) (32S15) Complex surface and hypersurface singularities (32S25) Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants (32S50)

Uses Software

SINGULAR

Cites Work

The Invariance of Milnor's Number Implies the Invariance of the Topological Type
The Invariance of Milnor's Number Implies Topological Triviality
The Multiplicity of Isolated Two-Dimensional Hypersurface Singularities: Zariski Problem
Bilipschitz Invariance of the Multiplicity
APPROXIMATIONS OF NON-ISOLATED SINGULARITIES OF FINITE CODIMENSION WITH RESPECT TO AN ISOLATED COMPLETE INTERSECTION SINGULARITY
On the Topology of Algebroid Singularities
Topological Triviality of μ-Constant Deformations of Type f (x ) + tg (x )
Multiplicity and degree as bi-Lipschitz invariants for complex sets
The link of {f(x, y) + zn = 0} and Zariski's conjecture
A Characteristic Number for Links of Surface Singularities
Seiberg–Witten Invariants and Surface Singularities. II: Singularities with Good C ^* ‐Action
Hypersurface Singularities with 2-Dimensional Critical Locus
A New Conjecture, a New Invariant, and a New Non-splitting Result
HOMOTOPICALLY TRIVIAL DEFORMATIONS
Reduction Theorem for Lattice Cohomology
Monodromy and the Lefschetz fixed point formula
Milnor Fibre Homology via Deformation
Links and analytic invariants of superisolated singularities
HEEGAARD FLOER HOMOLOGY AND RATIONAL CUSPIDAL CURVES
Equisingularity at the normalisation
Singular Points of Complex Hypersurfaces. (AM-61)
Some open questions in the theory of singularities
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
SINGULAR
Bi-Lipschitz homeomorphic subanalytic sets have bi-Lipschitz homeomorphic tangent cones
Logarithmic geometry and the Milnor fibration
A note on a topological approach to the \(\mu\)-constant problem in dimension 2
On a question of B. Teissier
Some special cases of Bobadilla's conjecture
The Seiberg-Witten invariants of negative definite plumbed 3-manifolds
Lefschetz numbers of iterates of the monodromy and truncated arcs
Dualität in der lokalen Kohomologie isolierter Singularitäten
The monodromy of a series of hypersurface singularities
Anticanonical models of rational surfaces
The Lê varieties. II
On Steenbrink's conjecture
The Lê varieties. I
Moment-angle complexes, monomial ideals and Massey products
Lattice cohomology of normal surface singularities
Topological triviality of deformations of functions and Newton filtrations
Conjugaison topologique des germes de fonctions holomorphes à singularité isolée en dimension trois
Constant Milnor number implies constant multiplicity for quasihomogeneous singularities
The \(\mu\)-constant stratum is not smooth
Some classes of line singularities
Threefolds and deformations of surface singularities
Some remarks on the geometry and classification of germs of maps from surfaces to 3-space
Topological types of complex isolated hypersurface singularities
The topology of normal singularities of an algebraic surface and a criterion for simplicity
The Milnor number and deformations of complex curve singularities
Topological type in families of germs
Calcul du nombre de cycles evanouissants d'une hypersurface complexe
Description of deformations with constant Milnor number for homogeneous functions
Polyedres de Newton et nombres de Milnor
Les conditions de Whitney impliquent `\(\mu(*)\) constant'
La fonction zeta d'une monodromie
Local normal forms of functions
Bifurcations, Dynkin diagrams, and modality of isolated singularities
\(C^n\) preservation of multiplicity
Topological type of isolated critical points
On the bifurcation of the multiplicity and topology of the Newton boundary
Topological properties of certain singularities with critical locus a 2- dimensional complete intersection
Torsion invariants of Spin\(^c\)-structures on 3-manifolds
Seiberg-Witten invariants and surface singularities
Links of rational singularities, L-spaces and LO fundamental groups
Holomorphic disks and topological invariants for closed three-manifolds
Homeomorphic graph manifolds: A contribution to the \(\mu\) constant problem
Classification of topological types of isolated quasihomogeneous two- dimensional hypersurface singularities
The relation between topological and algebro-geometric equisingularities according to Zariski
Relative morsification theory
On \((-P\cdot P)\)-constant deformations of Gorenstein surface singularities
Lê cycles and hypersurface singularities
Advances and improvements in the theory of standard bases and syzygies
The Nash problem for surfaces
Topology of hypersurface singularities with 3-dimensional critical set
Vanishing cycles, plane curve singularities and framed mapping class groups
Cohomology of contact loci
Multiplicity of singularities is not a bi-Lipschitz invariant
Computing motivic zeta functions on log smooth models
Topological equisingularity of hypersurfaces with 1-dimensional critical set
Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink
Beispiele zur Differentialtopologie von Singularitäten
On irreducible 3-manifolds which are sufficiently large
Eine Klasse von 3-dimensionalen Mannigfaltigkeiten. I, II
An algebraic classification of some knots of codimension two
Normal cones in analytic Whitney stratifications
Quasihomogeneous isolated singularities of hyperplanes.
Answers to some equisingularity questions
Floer cohomology, multiplicity and the log canonical threshold
Canonical splittings of groups and 3-manifolds
Lipschitz regular complex algebraic sets are smooth
On homotopy types of complements of analytic sets and Milnor fibres
Milnor Number of Weighted-Le-Yomdin Singularities
Non-formality of Milnor fibres of line arrangements
Notes on the Classification of Singularities
A Calculus for Plumbing Applied to the Topology of Complex Surface Singularities and Degenerating Complex Curves
Sur la condition de Thom stricte pour un morphisme analytique complexe
ON RATIONAL CUSPIDAL PROJECTIVE PLANE CURVES
The Lê numbers of the square of a function and their applications
Numerische Charakterisierung Quasihomogener GORENSTEIN-Kurvensingularitäten
Finite Determinacy of Functions with Non-Isolated Singularities
Topologically Trivial Deformations of Isolated Quasihomogeneous Hypersurface Singularities are Equimultiple
Topological types and multiplicities of isolated quasi-homogeneous surface singularities
On Equimultiple Subvarieties of Algebroid Hypersurfaces

This page was built for publication: Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR)