Flat 3-webs of degree one on the projective plane

Beltrán, Andrés Chaves; Luza, Maycol Falla; Marı́n, David

doi:10.5802/afst.1424

Cited by 4 publications

(4 citation statements)

References 6 publications

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“…These foliations are called convex. From these works ([4,Corollary 4.7]) and from Theorem A we deduce the classification, up to automorphism of P 2 C , of convex foliations of degree 3 on P 2 C .…”

Section: Introductionmentioning

confidence: 93%

“…-Up to automorphism of P 2 C the foliations F 1 and F 2 are the only foliations that realize the minimal dimension of orbits in degree 3. A. BELTRÁN, M. FALLA LUZA and D. MARÍN have shown in [4] that FP(3) contains the set of foliations F ∈ F(3) whose leaves which are not straight lines do not have inflection points. These foliations are called convex.…”

Section: Introductionmentioning

confidence: 99%

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Classification of foliations of degree three on $\mathbb{P}^{2}_{\mathbb{C}}$ with a flat Legendre transform

Bedrouni,

Marín

2018

Preprint

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The set F(3) of foliations of degree three on the complex projective plane can be identified with a Zariski's open set of a projective space of dimension 23 on which acts Aut(P 2 C ). The subset FP(3) of F(3) consisting of foliations of F(3) with a flat Legendre transform (dual web) is a Zariski closed subset of F(3). We classify up to automorphism of P 2 C the elements of FP(3). More precisely, we show that up to automorphism there are 16 foliations of degree three with a flat Legendre transform. From this classification we deduce that FP(3) has exactly 12 irreducible components. We also deduce that up to automorphism there are 4 convex foliations of degree three on P 2 .

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Classification of foliations of degree three on $\mathbb{P}^{2}_{\mathbb{C}}$ with a flat Legendre transform

Bedrouni,

Marín

2018

Preprint

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“…La Proposition 3.2 de [3] est un critère de la platitude de la transformée de LEGENDRE d'un feuilletage homogène de degré 3. Notre premier résultat généralise ce critère en degré arbitraire.…”

Section: éTude De La Platitude Du Tissu Dual D'un Feuilletage Homogèneunclassified

Tissus plats et feuilletages homogènes sur le plan projectif

Bedrouni¹,

Marín²

2016

Preprint

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Le but de ce travail est d'étudier les feuilletages du plan projectif complexe ayant une transformée de LEGENDRE (tissu dual) plate. Nous établissons quelques critères effectifs de la platitude du d-tissu dual d'un feuilletage homogène de degré d et nous décrivons quelques exemples explicites. Ces résultats nous permettent de montrer qu'à automorphisme de P 2 C près il y a 11 feuilletages homogènes de degré 3 ayant cette propriété. Nous verrons aussi qu'il est possible, sous certaines hypothèses, de ramener l'étude de la platitude du tissu dual d'un feuilletage inhomogène au cadre homogène. Nous obtenons quelques résultats de classification de feuilletages à singularités non-dégénérées et de transformée de LEGENDRE plate.

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“…TOME 0 (0), FASCICULE 0 A. Beltrán, M. Falla Luza and D. Marín have shown in [4] that FP(3) contains the set of foliations F ∈ F(3) whose leaves which are not straight lines do not have inflection points. These foliations are called convex.…”

Section: Introductionmentioning

confidence: 99%