Topological type of discriminants of some special families

Evelia R. García Barroso; M. Fernando Hernández Iglesias

doi:10.1007/s10998-021-00410-0

Topological type of discriminants of some special families

Evelia R. García Barroso, M. Fernando Hernández Iglesias

Research output: Contribution to journal › Article › peer-review

Abstract

We will describe the topological type of the discriminant curve of the morphism (ℓ, f) , where ℓ is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.

Original language	English
Journal	Periodica Mathematica Hungarica
DOIs	https://doi.org/10.1007/s10998-021-00410-0
State	Accepted/In press - 2021
Externally published	Yes

Bibliographical note

Funding Information:
Evelia R. García Barroso was partially supported by the Spanish Project MICINN PID2019-105896GB-I00.

Publisher Copyright:
© 2021, The Author(s).

Keywords

Discriminant curve
Milnor number
Newton polygon
Nondegenerate singularity
Tjurina number
Zariski invariant

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10.1007/s10998-021-00410-0

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keywords = "Discriminant curve, Milnor number, Newton polygon, Nondegenerate singularity, Tjurina number, Zariski invariant",

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AU - García Barroso, Evelia R.

AU - Hernández Iglesias, M. Fernando

PY - 2021

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N2 - We will describe the topological type of the discriminant curve of the morphism (ℓ, f) , where ℓ is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.

AB - We will describe the topological type of the discriminant curve of the morphism (ℓ, f) , where ℓ is a smooth curve and f is an irreducible curve (branch) of multiplicity less than five or a branch such that the difference between its Milnor number and Tjurina number is less than 3. We prove that for a branch of these families, the topological type of the discriminant curve is determined by the semigroup, the Zariski invariant and at most two other analytical invariants of the branch.

KW - Discriminant curve

KW - Milnor number

KW - Newton polygon

KW - Nondegenerate singularity

KW - Tjurina number

KW - Zariski invariant

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DO - 10.1007/s10998-021-00410-0

M3 - Artículo

AN - SCOPUS:85114392108

SN - 0031-5303

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

ER -

Topological type of discriminants of some special families

Abstract

Bibliographical note

Keywords

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