Characteristic Classes

DOI10.1007/978-3-030-95760-5_5zbMath1506.14001OpenAlexW4285224651MaRDI QIDQ5050032

Jean-Paul Brasselet

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_5

zbMATH Keywords

Chern classSegre classThom polynomialStiefel-Whitney classPontryagin classChern-Schwartz-MacPherson classcharacteristic classes of singular varietiesWu classlocal Euler obstructionHirzebruch theorymotivic Chern classstringy Chern class

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Theory of singularities and catastrophe theory (58Kxx) Complex singularities (32Sxx) Local theory in algebraic geometry (14Bxx)

Related Items (1)

Segre Classes and Invariants of Singular Varieties

Uses Software

• Macaulay2
• CSM-A
• CharacteristicClasses
• Book3264Examples
• MaximumLikelihoodObstructionFunction

Cites Work

• Milnor numbers and Euler obstruction
• The local Euler obstruction and topology of the stabilization of associated determinantal varieties
• Richtungsfelder und Fernparallelismus in \(n\)-dimensionalen Mannigfaltigkeiten
• Products of cocycles and extensions of mappings
• On the product of sphere bundles and the duality theorem modulo two
• Quelques propriétés globales des variétés différentiables
• Characteristic classes of Hermitian manifolds
• An elementary proof of Euler's formula using Cauchy's method
• 3264 and All That
• Polar Varieties Revisited
• Multitoric surfaces and Euler obstruction of a function
• Splayed divisors and their Chern classes
• Euler obstruction and polar multiplicities of images of finite morphisms on ICIS
• Codimension Two Determinantal Varieties with Isolated Singularities
• Some notes on the Euler obstruction of a function
• The Euler obstruction and the Chern obstruction
• Stiefel–Whitney numbers for singular varieties
• The Euler Characteristic of a Generic Wavefront in a 3-Manifold
• TWISTED TOPOLOGICAL STRUCTURES RELATED TO M-BRANES II: TWISTED Wu ANDWu^cSTRUCTURES
• Milnor Number Equals Tjurina Number for Functions on Space Curves
• Motivic characteristic classes
• Characteristic classes of mixed Hodge modules
• Stiefel-Whitney Homology Classes of Quasi-Regular Cell Complexes
• La théorie des classes de Chern
• Witt Spaces: A Geometric Cycle Theory for KO-Homology at Odd Primes
• Equivariant Chern classes of singular algebraic varieties with group actions
• Intersection homology with field coefficients:K-Witt spaces andK-Witt bordism
• THE EULER OBSTRUCTION AND BRUCE-ROBERTS' MILNOR NUMBER
• EULER OBSTRUCTION, POLAR MULTIPLICITIES AND EQUISINGULARITY OF MAP GERMS IN $\mathcal{O}(n,p), n < p$
• Characteristic Classes of Singular Toric Varieties
• Macpherson's chern classes of singular algebraic varieties
• HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES
• Singular Chern Classes of Schubert Varieties via Small Resolution
• The Flaw in Euler's Proof of His Polyhedral Formula
• Une nouvelle preuve de la concordance des classes définies par M.-H. Schwartz et par R. MacPherson
• ORIENTED BIVARIANT THEORIES, I
• Sur la formule de Gonzalez-verdier
• Polar Classes and Segre Classes on Singular Projective Varieties
• Characteristic classes, singular embeddings, and intersection homology
• Espaces de Thom et contre-exemples de J.L. Verdier et M. Goresky
• Algebraic Cycles and Intersection Homology
• Categorical framework for the study of singular spaces
• Stratifiable Maps and Topological Invariants
• A combinatorial formula for the Pontrjagin classes
• Characteristic Classes. (AM-76)
• Index theorem for a maximally overdetermined system of linear differential equations
• A Formula for Stiefel-Whitney Homology Classes
• Polar classes of singular varieties
• AN ADJUNCTION FORMULA FOR LOCAL COMPLETE INTERSECTIONS
• Chern classes for singular hypersurfaces
• Birational Calabi--Yau n-folds have equal Betti numbers
• Genera of algebraic varieties and counting of lattice points
• Curvature Measures of Subanalytic Sets
• Euler obstruction and Lipschitz-Killing curvatures
• The Pro-Chern-Schwartz-MacPherson class for DM stacks
• New orientifold weak coupling limits in F-theory
• The vanishing Euler characteristic of an isolated determinantal singularity
• Algorithms to compute the topological Euler characteristic, Chern-Schwartz-MacPherson class and Segre class of projective varieties
• Motivic and derived motivic Hirzebruch classes
• Minimal Whitney stratification and Euler obstruction of discriminants
• Stiefel-Whitney homology classes of \(Z^ 2\)-Poincaré-Euler spaces
• On indices of 1-forms on determinantal singularities
• A geometric degree formula for \(A\)-discriminants and Euler obstructions of toric varieties
• Equivariant Hirzebruch class for singular varieties
• Lê cycles and Milnor classes
• Erratum to: ``Lê cycles and Milnor classes
• On the triangulation of subanalytic morphisms.
• Intersection homology. II
• Linking pairings on singular spaces
• Cycle maximal et invariant d'Euler local des singularités isolées de surfaces
• Modification systems and integration in their Chow groups
• Hirzebruch classes and motivic Chern classes.
• Chern classes for singular varieties, revisited.
• Stringy Chern classes of singular varieties
• Limits of Chow groups, and a new construction of Chern-Schwartz-MacPherson classes
• On the uniqueness of bivariant Chern class and bivariant Riemann--Roch transformations
• Wu numbers of singular spaces
• Intersection homology Poincaré spaces and the characteristic variety theorem
• Hodge genera and characteristic classes of complex algebraic varieties
• The local Euler obstruction of a function
• Donaldson-Thomas type invariants via microlocal geometry
• Index formula for MacPherson cycles of affine algebraic varieties
• On Grothendieck transformations in Fulton-MacPherson's bivariant theory
• Cobordism of singular maps
• Vector fields on singular varieties
• Axioms for Stiefel-Whitney homology classes of \({\mathbb{Z}}_ 2\)-Euler spaces
• Stiefel-Whitney homology classes and homotopy type of Euler spaces
• Characteristic varieties and vanishing cycles
• Critical points of functions on analytic varieties
• Topological quantum field theory
• Universal Wu classes
• A formula for Segre classes of singular projective varieties
• Cohomologie-Operationen und charakteristische Klassen. (Cohomology operations and characteristic classes)
• Intersection homology theory
• Multiple-point formulas. I: Iteration
• Variétés polaires locales et classes de Chern des variétés singulieres
• Singular spaces, characteristic classes, and intersection homology
• Singularity theory and its applications, Warwick 1989, Part I: Geometric aspects of singularities. Proceedings of a symposium, held at the University of Warwick, UK, during the academic year 1988--89
• \(\mathcal A\)-codimension and the vanishing topology of discriminants
• Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten
• Chern classes for singular algebraic varieties
• Characteristic classes of flags of foliations
• Riemann-Roch for singular varieties
• Stratifications de Whitney et théorème de Bertini-Sard
• On a Verdier-type Riemann-Roch for Chern-Schwartz-MacPherson class
• Curvature measures and Chern classes of singular varieties
• On semi- and subanalytic geometry
• Five-brane effective action in \(M\)-theory
• On the implementation of Lie group methods on the Stiefel manifold
• Euler obstruction and indices of vector fields
• Bivariant Chern-Schwartz-MacPherson classes with values in Chow groups
• On the uniqueness problem of bivariant Chern classes
• Euler obstruction of essentially isolated determinantal singularities
• Chern classes and characteristic cycles of determinantal varieties
• On the contribution of Wu Wen-Tsün to algebraic topology
• Stringy Chern classes of singular toric varieties and their applications
• Stability of the Euler obstruction of a function
• Chern-Schwartz-MacPherson classes of degeneracy loci
• Product formula for twisted MacPherson classes
• Sur la topologie de certains espaces homogenes
• Lifting of algebraic cycles and associated homomorphisms in intersection homology.
• Characteristic forms and geometric invariants
• Computing characteristic classes of projective schemes.
• Elliptic genera of singular varieties.
• Addendum to: ``Bivariant Chern-Schwartz-MacPherson classes with values in Chow groups
• Remarks on the relations between the Italian and American schools of algebraic geometry in the first decades of the 20th century
• Lê cycles and hypersurface singularities
• Stiefel-Whitney homology classes and Euler subspaces
• Singular schemes of hypersurfaces
• Hypercohomology of Milnor fibres
• Polar multiplicities and Euler obstruction for ruled surfaces
• Toric surfaces, vanishing Euler characteristic and Euler obstruction of a function
• Marie-Hélène Schwartz and radial vector fields, a mathematical course
• Brasselet number and function-germs with a one-dimensional critical set
• Image Milnor number formulas for weighted-homogeneous map-germs
• Elliptic classes of Schubert varieties
• Classes caractéristiques pour les cônes projectifs et homologie d'intersection. (Characteristic classes for projective cones and intersection homology)
• The index of a holomorphic flow with an isolated singularity
• Brasselet number and Newton polygons
• Note on MacPherson's local Euler obstruction
• An implementation of the Lê-Teissier method for computing local Euler obstructions
• The Euler obstruction and torus action
• Characteristic classes of symmetric products of complex quasi-projective varieties
• The Euler obstruction of a function on a determinantal variety and on a curve
• Local Euler obstructions of toric varieties
• Lê-Greuel type formula for the Euler obstruction and applications
• Motivic bivariant characteristic classes
• Quadratic functions in geometry, topology, and \(M\)-theory
• Bivariant Chern classes for morphisms with nonsingular target varieties
• Cobordism of maps
• Stiefel-Whitney homology classes
• Global Euler obstruction and polar invariants
• Radial index and Euler obstruction of a 1-form on a singular variety
• Classes de Chern des intersections complètes locales
• Multiplicity of Functions On Singular Varieties
• Functions on Space Curves
• Remarks on Ginzburg’s bivariant Chern classes
• Equivariant Chern-Schwartz-MacPherson classes in partial flag varieties: interpolation and formulae
• Equivariant Characteristic Classes of Singular Complex Algebraic Varieties
• On Cappell-Shaneson's Homology L-Classes of Singular Algebraic Varieties
• Differential forms with logarithmic poles and Chern-Schwartz-MacPherson classes of singular varieties
• On Ginzburg’s bivariant Chern classes
• EULER OBSTRUCTION AND DEFECTS OF FUNCTIONS ON SINGULAR VARIETIES
• Multisingularities, cobordisms, and enumerative geometry
• Looking at bent wires – -codimension and the vanishing topology of parametrized curve singularities
• Chern-Schwartz-Macpherson Classes and the Euler Characteristic of Degeneracy Loci and Special Divisors
• THE BRUCE-ROBERTS NUMBER OF A FUNCTION ON A WEIGHTED HOMOGENEOUS HYPERSURFACE
• Global Euler obstruction, global Brasselet numbers and critical points
• Chern Classes and Transversality for Singular Spaces
• Motivic Chern classes and K‐theoretic stable envelopes
• Segre Classes and Invariants of Singular Varieties
• Milnor Number and Chern Classes for Singular Varieties: An Introduction
• Residues and Hyperfunctions
• Characteristic Classes of Orbit Stratifications, the Axiomatic Approach
• Elliptic classes of Schubert varieties via Bott–Samelson resolution
• Local Euler obstructions and Chern–Mather classes of determinantal varieties
• Motivic Chern classes of configuration spaces
• Motivic Milnor classes
• MOTIVIC BIVARIANT CHARACTERISTIC CLASSES AND RELATED TOPICS
• EQUIVARIANT CHERN CLASSES AND LOCALIZATION THEOREM
• THE CHERN–SCHWARTZ–MACPHERSON CLASS OF AN EMBEDDABLE SCHEME
• Cobordism of maps of locally orientable Witt spaces
• Singularities of Mappings
• Topological field theories on manifolds with Wu structures
• Poincaré-Hopf theorems on singular spaces
• The Multiplicity Polar Theorem, Collections of 1-forms and Chern Numbers
• Nearby cycles and characteristic classes of singular spaces
• Stiefel-Whitney classes and the conormal cycle of a singular variety
• Invariants, equisingularity and Euler obstruction of map germs from ℂⁿto ℂⁿ
• The Arithmetical Invariants of Algebraic Loci
• On the Characteristic Classes of Riemannian Manifolds
• Computing Euler Obstruction Functions Using Maximum Likelihood Degrees
• Characteristic Classes of Singular Varieties
• Lectures on Characteristic Classes of Constructible Functions
• Thom polynomials, symmetries and incidences of singularities
• Cellular morphism and bivariant Chern classes
• An application of bivariant theory to Milnor classes
• 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
• 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Characteristic Classes