Codimension one distributions of degree 2 on the three-dimensional projective space

Galeano, Hugo; Jardim, Marcos; Muniz, Alan

doi:10.1016/j.jpaa.2021.106840

Cited by 6 publications

(5 citation statements)

References 18 publications

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“…A complete classification of degree 2 codimension one distributions in P 3 has been given by Galeano, Jardim and Muniz in [29]. They prove the following result.…”

Section: Geometry Of Spaces Of Codimension One Degree 0 Distributionsmentioning

confidence: 86%

“…In [5] we have initiated a systematic study of codimension one holomorphic distributions on P 3 , analyzing the properties of their singular schemes and tangent sheaves and also we give a partial classification of distributions of degree ≤ 2. A complete classification of distributions of codimension 2 and degree 2 in P 3 was given by Galeano, Jardim and Muniz in [29]. They show that there are 17 different types of such distributions.…”

Section: Introductionmentioning

confidence: 99%

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On classification and moduli spaces of holomorphic distributions

Corrêa

2023

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“…A complete classification of degree 2 codimension one distributions in P 3 has been given by Galeano, Jardim and Muniz in [29]. They prove the following result.…”

Section: Geometry Of Spaces Of Codimension One Degree 0 Distributionsmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

On classification and moduli spaces of holomorphic distributions

Corrêa

2023

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“…They showed that there exists a quasi-projective variety that parametrizes isomorphism classes of distributions, on a complex projective manifold whose tangent sheaves have a fixed Hilbert polynomial. In [37] Galeano, Jardim and Muniz provide a classification of distributions of degree 2 in P 3 . In [22] the authors give the first step to the study foliations by curves on the three-dimensional projective space with no isolated singularities.…”

Section: Introductionmentioning

confidence: 99%

Dimension two holomorphic distributions on four-dimensional projective space

Calvo-Andrade¹,

Corrêa²,

Fonseca-Quispe³

2022

Preprint

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We study two-dimensional holomorphic distributions on P 4 . We classify dimension two distributions, of degree at most 2, with either locally free tangent sheaf or locally free conormal sheaf and whose the singular scheme has pure dimension one. We show that the corresponding sheaves are split. Next, we investigate the geometry of such distributions, studying from maximally non-integrable to integrable distributions. In the maximally non-integrable case, we show that the distribution is either of Lorentzian type or a push-forward by a rational map of the Cartan prolongation of a singular contact struture on a weighted projective 3-fold. We study distributions of dimension two in P 4 whose the conormal sheaf are the Horrocks-Mumford sheaves, describing the numerical invariants of their singular schemes which are smooth and connected. Such distributions are maximally non-integrable, uniquely determined by their singular schemes and invariant by a group H 5 ⋊ SL(2, Z 5 ) ⊂ Sp(4, Q), where H 5 is the Heisenberg group of level 5. We prove that the moduli spaces of Horrocks-Mumford distributions are irreducible quasi-projective varieties and we determine their dimensions. Finally, we observe that the space of codimension one distributions, of degree d ≥ 6, on P 4 have a family of degenerated flat holomorphic Riemannian metrics. Moreover, the degeneracy divisors of such metrics consists of codimension one distributions invariant by H 5 ⋊ SL(2, Z 5 ) and singular along a degenerate abelian surface with (1, 5)-polarization and level-5-structure.

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“…Distribution hom♣F , TP 3 q Saturation F ♣0, In this section, we provide explicit descriptions of the moduli spaces of distributions. We denote the moduli space D P with P ✏ 1 3 ♣t 3q♣t 2q♣t 1q 1 2 ♣t 2q♣t 1q♣2 ✁ dq ✁ ♣t To use the Lemma 1.6.4 we need the next proposition whose proof can be found in [8]. for every k ➙ 1.…”

Section: Non-existence Resultsmentioning

confidence: 99%

“…The values in boldface are realized and the description can be found in [18]. The values in blue and red were recently proved by Jardim, the results can be found in [8]. The description of the colors mean: for the values in red there are no distributions; The values in blue are the ones that.…”

Section: Classification Of Codimension One Degree 2 Distributionsmentioning

confidence: 89%

Codimension one distributions of degree 2 on the projective three-space

Anaya¹

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Agradezco a Dios por haberme traído a este país tan hermoso lleno de gente linda y amable, por haberme sustentado, dirigido y guardado todos estos años que no fueron nada fácil. A mis padres, por los valores enseñados y el amor al trabajo, que hoy están rindiendo frutos una vez más. A mi amada esposa Cindy Margoth y a mi preciosa hija brasilera Priscila, por la compañía y el amor constante.Ao professor Marcos Benevenuto Jardim, eu agradeço infinitamente, você me ajudou em um momento difícil, você estendeu a sua mão e confiou em mim, você foi mais do que um orientador, você é o melhor, Deus te abençoe sempre.Ao meu amigo Douglas Manoel Guimarães, você me ajudou muito no início desta jornada, muito obrigado. Ao meu amigo Danilo Rezende, muito obrigado pela sua ajuda. Ao meu amigo Allan Suverov, obrigado pela força.A mi hermano Robert quien me sugirió estudiar en la Unicamp, su esposa Lina y su hija Válery, que estuvieron tambien en esta jornada aquí en Brasil, por la compañía y su amistad. A toda mi familia en Colombia, mis hermanas Katy y Ketty.A mis amigos de vieja guardia, que fueron un apoyo y sustento contante desde

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Codimension one distributions of degree 2 on the three-dimensional projective space

Cited by 6 publications

References 18 publications

On classification and moduli spaces of holomorphic distributions

On classification and moduli spaces of holomorphic distributions

Dimension two holomorphic distributions on four-dimensional projective space

Codimension one distributions of degree 2 on the projective three-space

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