Slicing Corank 1 Map Germs From C2 to C3

Marar, Washington Luiz; Nuño–Ballesteros, J. J.

doi:10.1093/qmath/hat061

Cited by 16 publications

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“…be a stabilisation of f , for s = 0. By [9], f is a 1-parameter unfolding of the plane curve A 4 , g(z) = (z 2 , z 5 ) and in fact, g is the transverse slice of f . Let M 3 (f s , (1, 1, 1)) ∪ M 2 (f s , (2)) be the 0-dimensional strata of X s .…”

Section: Examplesmentioning

confidence: 99%

A Lê-Greuel type formula for the image Milnor number

Nuño–Ballesteros¹,

Pallarés-Torres²

2019

Hokkaido Math. J.

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Let f : (C n , 0) → (C n+1 , 0) be a corank 1 finitely determined map germ. For a generic linear form p : (C n+1 , 0) → (C, 0) we denote by g : (C n−1 , 0) → (C n , 0) the transverse slice of f with respect to p. We prove that the sum of the image Milnor numbers µI (f ) + µI (g) is equal to the number of critical points of the stratified Morse function p|X s : Xs → C, where Xs is the disentanglement of f (i.e., the image of a stabilisation fs of f ).2000 Mathematics Subject Classification. Primary 32S30; Secondary 32S05, 58K40.

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Section: Examplesmentioning

confidence: 99%

A Lê-Greuel type formula for the image Milnor number

Nuño–Ballesteros¹,

Pallarés-Torres²

2019

Hokkaido Math. J.

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“…In Marar and Nuño-Ballesteros (2014), the authors studied the transversal slice of a corank 1 map germ f : (C 2 , 0) → (C 3 , 0) (see Marar and Nuño-Ballesteros (2014), Sect. 3).…”

Section: Introductionmentioning

confidence: 99%

On Invariants of Generic Slices of Weighted Homogeneous Corank 1 Map Germs from the Plane to 3-Space

Silva

2020

Bull Braz Math Soc, New Series

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In this work, we consider a quasi-homogeneous, corank 1, finitely determined map germ f from (C 2 , 0) to (C 3 , 0). We consider the invariants m(f (D(f))) and J , where m(f (D(f))) denotes the multiplicity of the image of the double point curve D(f) of f and J denotes the number of tacnodes that appears in a stabilization of the transversal slice curve of f (C 2). We present formulas to calculate m(f (D(f))) and J in terms of the weights and degrees of f .

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“…[8] Corollary 4.7) Let F be a 1-parameter unfolding of a finitely determined map germ f : (C 2 , 0) → (C 3 , 0) with corank 1. Then, the following conditions are equivalent:…”

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confidence: 99%

Whitney equisingularity of families of surfaces in ℂ³

Ruas¹,

Silva²

2018

Math. Proc. Camb. Phil. Soc.

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In this work, we study families of singular surfaces in C 3 parametrized by A-finitely determined map germs. We consider the topological triviality and Whitney equisingularity of an unfolding F of a finitely determined map germ f : (C 2 , 0) → (C 3 , 0). We investigate the following conjecture: topological triviality implies Whitney equisingularity of the unfolding F ? We provide a complete answer to this conjecture, given counterexamples showing how the conjecture can be false. * M.A.S. Ruas: ICMC, Universidade de São Paulo, Av. do Trabalhador São

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Slicing Corank 1 Map Germs From C2 to C3

Cited by 16 publications

References 0 publications

A Lê-Greuel type formula for the image Milnor number

A Lê-Greuel type formula for the image Milnor number

On Invariants of Generic Slices of Weighted Homogeneous Corank 1 Map Germs from the Plane to 3-Space

Whitney equisingularity of families of surfaces in ℂ³

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Slicing Corank 1 Map Germs From C2 to C3

Cited by 16 publications

References 0 publications

A Lê-Greuel type formula for the image Milnor number

A Lê-Greuel type formula for the image Milnor number

On Invariants of Generic Slices of Weighted Homogeneous Corank 1 Map Germs from the Plane to 3-Space

Whitney equisingularity of families of surfaces in ℂ3

Contact Info

Product

Resources

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Whitney equisingularity of families of surfaces in ℂ³