On Briançon–Skoda theorem for foliations

Arturo Fernández-Pérez; Evelia R. García Barroso; Nancy Saravia-Molina

doi:10.1016/j.exmath.2023.07.001

On Briançon–Skoda theorem for foliations

Arturo Fernández-Pérez, Evelia R. García Barroso, Nancy Saravia-Molina

Sección de Matemáticas

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Resumen

We generalize Mattei's result relative to the Briançon–Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relationships between the Milnor and Tjurina numbers of foliations of second type, inspired by the results obtained by Liu for complex hypersurfaces and we determine a lower bound for the global Tjurina number of an algebraic curve.

Idioma original	Inglés
Número de artículo	125512
Publicación	Expositiones Mathematicae
Volumen	41
N.º	4
DOI	https://doi.org/10.1016/j.exmath.2023.07.001
Estado	Publicada - dic. 2023

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title = "On Brian{\c c}on–Skoda theorem for foliations",

abstract = "We generalize Mattei's result relative to the Brian{\c c}on–Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relationships between the Milnor and Tjurina numbers of foliations of second type, inspired by the results obtained by Liu for complex hypersurfaces and we determine a lower bound for the global Tjurina number of an algebraic curve.",

keywords = "Brian{\c c}on–Skoda theorem, Holomorphic foliations, Milnor number, Tjurina number",

author = "Arturo Fern{\'a}ndez-P{\'e}rez and {Garc{\'i}a Barroso}, {Evelia R.} and Nancy Saravia-Molina",

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AU - Fernández-Pérez, Arturo

AU - García Barroso, Evelia R.

AU - Saravia-Molina, Nancy

PY - 2023/12

Y1 - 2023/12

N2 - We generalize Mattei's result relative to the Briançon–Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relationships between the Milnor and Tjurina numbers of foliations of second type, inspired by the results obtained by Liu for complex hypersurfaces and we determine a lower bound for the global Tjurina number of an algebraic curve.

AB - We generalize Mattei's result relative to the Briançon–Skoda theorem for foliations to the family of foliations of the second type. We use this generalization to establish relationships between the Milnor and Tjurina numbers of foliations of second type, inspired by the results obtained by Liu for complex hypersurfaces and we determine a lower bound for the global Tjurina number of an algebraic curve.

KW - Briançon–Skoda theorem

KW - Holomorphic foliations

KW - Milnor number

KW - Tjurina number

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DO - 10.1016/j.exmath.2023.07.001

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JO - Expositiones Mathematicae

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ER -

On Briançon–Skoda theorem for foliations

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