Distinguished Bases and Monodromy of Complex Hypersurface Singularities

DOI10.1007/978-3-030-53061-7_8zbMath1475.32019arXiv1905.12435OpenAlexW2947125792MaRDI QIDQ5014458

Wolfgang Ebeling

Publication date: 2 December 2021

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

Full work available at URL: https://arxiv.org/abs/1905.12435

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces (32-02) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Fibrations, degenerations in algebraic geometry (14D06) Complex surface and hypersurface singularities (32S25) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40)

Related Items

Deformation and Smoothing of Singularities, Milnor’s Fibration Theorem for Real and Complex Singularities

Cites Work

• A categorification of non-crossing partitions
• A generalized construction of mirror manifolds
• A few problems on monodromy and discriminants
• On decompositions of a cyclic permutation into a product of a given number of permutations
• On the Hurwitz action in finite Coxeter groups
• An arithmetic characterisation of the symmetric monodromy groups of singularities
• Derived equivalences from mutations of quivers with potential
• Topological classification of trigonometric polynomials and combinatorics of graphs with an equal number of vertices and edges
• Addendum zu der Arbeit ``Ausgezeichnete Basen von Milnorgittern einfacher Singularitäten von E. Voigt. (Addendum to the paper ``Distinguished bases of Milnor lattices of simple singularities by E. Voigt)
• Fifteen characterizations of rational double points and simple critical points
• Milnor lattices and geometric bases of some special singularities
• The monodromy groups of critical points of functions. II
• Skew-symmetric vanishing lattices and their monodromy groups
• A characterization of the intersection form of a Milnor's fiber for a function with an isolated critical point
• Geometry of bifurcation diagrams
• Hurwitz orbits of primitive factorizations of a Coxeter element.
• Exceptional sequences and clusters. (With an appendix with Hugh Thomas).
• Extended affine root systems. I: Coxeter transformations
• Ausgezeichnete Basen von Milnorgittern einfacher Singularitäten
• Distribution of critical values of miniversal deformations of parabolic singularities
• Skew-symmetric vanishing lattices and their monodromy groups. II
• Twisted Picard-Lefschetz formulas
• Criteria for topological equivalence and a Lê-Ramanujam theorem for three complex variables
• Polar curves and intersection matrices of singularities
• Invariant theory for generalized root systems
• Quadratische Formen und Monodromiegruppen von Singularitäten
• Erzeugung ganzzahliger orthogonaler Gruppen durch Spiegelungen
• Tresses, monodromie et le groupe symplectique
• The topology of complex projective varieties after S. Lefschetz
• Monodromy groups of critical point of functions
• Distinguished bases of simple singularities
• Automorphisms of the complement of the bifurcation set of functions for simple singularities
• Einfach-elliptische Singularitäten
• Die Homologie isolierter Singularitäten
• Intersection matrices for certain singularities of functions of two variables
• Dynkin diagrams for unimodal singularities
• Dynkin diagrams for singularities of functions of two variables
• Le groupe de monodromie du déploiement des singularités isolées de courbes planes. I
• La fonction zeta d'une monodromie
• The monodromy of weighted homogeneous singularities
• Bifurcations, Dynkin diagrams, and modality of isolated singularities
• On the semi-universal deformation of a simple-elliptic hypersurface singularity part II: The discriminant
• On the monodromy group of plane curve singularities
• Sur les valeurs propres de la transformation de Coxeter
• On classification of \(N=2\) supersymmetric theories
• On Coxeter-Dynkin diagrams of hypersurface singularities
• Coxeter-Dynkin diagrams of partially ordered sets and A'Campo-Gusein-Zade diagrams of simple singularities
• The complement of the bifurcation variety of a simple singularity
• Braids and self-distributivity
• A note on distinguished bases of singularities
• Lyashko-Looijenga morphisms and submaximal factorizations of a Coxeter element
• Galois group of Looijenga-Lyashko mapping
• Killing and the Coxeter transformation of Kac-Moody algebras
• The monodromy groups of isolated singularities of complete intersections
• Rational surfaces with an anti-canonical cycle
• Normal forms for functions near degenerate critical points, the Weyl groups of A\(_k\), D\(_k\), E\(_k\) and lagrangian singularities
• The intersection matrix of Brieskorn singularities
• Intersection matrices for certain singularities
• A'Campo's theorem on the discriminant
• Characterization of simple Coxeter-Dynkin diagrams
• Combinatorial structure of Stokes regions of a simple singularity
• A geometric construction of Coxeter-Dynkin diagrams of bimodal singularities
• On multiplicities of the Lyashko-Looijenga mapping on discriminant strata
• Maximally-graded matrix factorizations for an invertible polynomial of chain type
• Fibered knots and algebraic singularities
• Finite complex reflection arrangements are \(K(\pi,1)\)
• Dual presentations of braid groups of affine type \(\widetilde A\).
• Beispiele zur Differentialtopologie von Singularitäten
• A note on curvature and fundamental group
• \(O(n)\)-manifolds, exotic spheres, and singularities
• Monodromy of isolated singularities of hypersurfaces
• Die Fundamentalgruppe des Raumes der regulären Orbits einer endlichen komplexen Spiegelungsgruppe
• Un résultat sur la monodromie. (A result on the monodromy)
• Les immeubles des groupes de tresses généralises
• Artin-Gruppen und Coxeter-Gruppen
• Séminaire de géométrie algébrique du Bois-Marie 1967--1969. Groupes de monodromie en géométrie algébrique (SGA 7 II) par P. Deligne et N. Katz. Exposés X à XXII
• Fundamental group of discriminant complements of Brieskorn-Pham polynomials
• Theory of braids
• A note on the transitive Hurwitz action on decompositions of parabolic Coxeter elements
• On the Coxeter transformation of an isolated singularity
• The dual braid monoid
• ON WEAKLY DISTINGUISHED BASES AND FREE GENERATING SETS OF FREE GROUPS
• On Basis-Conjugating Automorphisms of Free Groups
• Geometric bases and topological equivalence
• THE GEOMETRY OF BIFURCATION DIAGRAMS
• REMARKS ON THE STATIONARY PHASE METHOD AND COXETER NUMBERS
• CRITICAL POINTS OF SMOOTH FUNCTIONS AND THEIR NORMAL FORMS
• The Invariance of Milnor's Number Implies the Invariance of the Topological Type
• THE MONODROMY GROUPS OF ISOLATED SINGULARITIES OF HYPERSURFACES
• On $ q$-monodromy groups of singularities
• Toric duality, Seiberg duality and Picard‐Lefschetz transformations
• BRAID MONODROMY OF SOME BRIESKORN–PHAM SINGULARITIES
• Homological mirror symmetry for singularities
• THE TOPOLOGICAL PROPERTIES OF ISOLATED SINGULARITIES OF COMPLEX SPACES OF CODIMENSION ONE
• Singular Points of Complex Hypersurfaces. (AM-61)
• Formules de Picard-Lefschetz généralisées et ramification des intégrales
• Distinguished bases of non-simple 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