Join theorem for polar weighted homogeneous singularities

Cisneros‐Molina, José Luis

doi:10.1090/conm/475/09274

Cited by 40 publications

(57 citation statements)

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“…We say that the set of ρ-nonregular points 3 of an analytic mapping Ψ : U → R is the set of non-transversality between ρ and Ψ, i.e. M(Ψ) = { ∈ U : ρ Ψ}.…”

Section: Definition 12mentioning

confidence: 99%

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Singular open book structures from real mappings

2013

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“…We say that the set of ρ-nonregular points 3 of an analytic mapping Ψ : U → R is the set of non-transversality between ρ and Ψ, i.e. M(Ψ) = { ∈ U : ρ Ψ}.…”

Section: Definition 12mentioning

confidence: 99%

“…After [3] and [16], we call polar weighted-homogeneous if there are non-zero integers 1 and such that gcd ( 1 ) = 1 and…”

Section: Polar Weighted-homogeneous Mixed Functionsmentioning

confidence: 99%

Singular open book structures from real mappings

2013

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“…These polynomials were introduced by Cisneros-Molina in [4] following ideas from Ruas, Seade and Verjovsky in [22] and studied by Oka in [16] and [17]. Let ( p 1 , .…”

Section: Polar Weighted Homogeneous Polynomialsmentioning

confidence: 99%

“…We compute the Euler characteristic of F using the Join Theorem for polar weighted homogeneous polynomials [4,Th. 4.1], which is a generalisation of Oka's result (see [15,Th.…”

Section: Corollarymentioning

confidence: 99%

“…We show that its corresponding canonical class is not integral so the graph cannot be the dual graph of a resolution of a hypersurface singularity. For the case of different pages we use the Join Theorem of [4] to compute the Euler characteristic of the Milnor fibre and we apply the Laufer-Steenbrink formula to see that the Milnor fibre of F cannot appear as the Milnor fibre of a smoothing of a normal Gorenstein complex surface singularity.…”

Section: Introductionmentioning

confidence: 99%

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New open-book decompositions in singularity theory

Aguilar-Cabrera

2011

Geom Dedicata

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In this article, we study the topology of real analytic germs F : (C 3 , 0) → (C, 0) given by F(x, y, z) = x y(x p + y q ) + z r with p, q, r ∈ N, p, q, r ≥ 2 and ( p, q) = 1. Such a germ gives rise to a Milnor fibration F |F| : S 5 \ L F → S 1 . We describe the link L F as a Seifert manifold and we show that in many cases the open-book decomposition of S 5 given by the Milnor fibration of F cannot come from the Milnor fibration of a complex singularity in C 3 .

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Thom property and Milnor–Lê fibration for analytic maps

Menegon

2023

Mathematische Nachrichten

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Let (X, 0) be the germ of either a subanalytic set or a complex analytic space , and let be a ‐analytic map‐germ, with or , respectively. When , there is a well‐known topological locally trivial fibration associated with f, called the Milnor–Lê fibration of f, which is one of the main pillars in the study of singularities of maps and spaces. However, when that is not always the case. In this paper, we give conditions which guarantee that the image of f is well‐defined as a set‐germ, and that f admits a Milnor–Lê fibration. We also give conditions for f to have the Thom property. Finally, we apply our results to mixed function‐germs of type on a complex analytic surface with arbitrary singularity.

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Join theorem for polar weighted homogeneous singularities

Cited by 40 publications

References 0 publications

Singular open book structures from real mappings

Singular open book structures from real mappings

New open-book decompositions in singularity theory

Thom property and Milnor–Lê fibration for analytic maps

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