Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space

We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic invariants of the conormal sheaves and singular schemes for su...

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Autores: Corrêa, M., Jardim, M., Marchesi, S.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/537052
Acesso em linha:http://hdl.handle.net/2072/537052
Access Level:acceso abierto
Palavra-chave:Chern classes
Holomorphic foliations by curves
moduli spaces
reflexive sheaves
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spelling Classification of the invariants of foliations by curves of low degree on the three-dimensional projective spaceCorrêa, M.Jardim, M.Marchesi, S.Chern classesHolomorphic foliations by curvesmoduli spacesreflexive sheavesWe study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic invariants of the conormal sheaves and singular schemes for such foliations by curves, up to degree 3. In particular, we prove that foliations by curves of degree 1 or 2 are contained in a pencil of planes or are Legendrian, and are given by the complete intersection of two codimension one distributions. Furthermore, we prove that the conormal sheaf of a foliation by curves of degree 3 with reduced singular scheme either splits as a sum of line bundles or is an instanton bundle. For degree larger than 3, we focus on two classes of foliations by curves, namely Legendrian foliations and those whose conormal sheaf is a twisted null-correlation bundle. We give characterizations of such foliations, describe their singular schemes and their moduli spaces. © 2023 Real Sociedad Matemática Española.Funding text 1: We would like to thank Israel Vainsencher and Alan Muniz for useful discussions. M. C. is grateful to Universidade Estadual de Campinas for its hospitality; he would like to thank the Universidade Federal de Minas Gerais, the institution he was affiliated with when this work started. S. M. would like to thank the Universidade Estadual de Campinas, the institution he was affiliated with when this work started. M. C. was supported by the CNPQ grants no. 202374/2018-1, 302075/2015-1, and 400821/2016-8; he was also supported by the FAPESP grant number 2015/20841-5; he is supported by the Prin 2022 Interactions between Geometric Structures and Function Theories, and is a member of INdAM-GNSAGA. M. J. is supported by the CNPQ grant no. 302889/2018-3 and the FAPESP Thematic Project 2018/21391-1. S. M. was partially supported by FAPESP grant number 2019/08279-0, by CNPQ grant no. 303075/2017-1, by PID2020-113674GB-I00, and by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M), and is a member of INdAM-GNSAGA. This work was also partially funded by CAPES - Finance Code 001.; Funding text 2: Funding. M. C. was supported by the CNPQ grants no. 202374/2018-1, 302075/2015-1, and 400821/2016-8; he was also supported by the FAPESP grant number 2015/20841-5; he is supported by the Prin 2022 Interactions between Geometric Structures and Function Theories, and is a member of INdAM-GNSAGA. M. J. is supported by the CNPQ grant no. 302889/2018-3 and the FAPESP Thematic Project 2018/21391-1. S. M. was partially supported by FAPESP grant number 2019/08279-0, by CNPQ grant no. 303075/2017-1, by PID2020-113674GB-I00, and by the Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M), and is a member of INdAM-GNSAGA. This work was also partially funded by CAPES - Finance Code 001.European Mathematical Society Publishing House2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion40 p.application/pdfhttp://hdl.handle.net/2072/537052RECERCAT (Dipòsit de la Recerca de Catalunya)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésRevista Matematica IberoamericanaL'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2072/5370522026-05-29T05:05:01Z
dc.title.none.fl_str_mv Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
title Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
spellingShingle Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
Corrêa, M.
Chern classes
Holomorphic foliations by curves
moduli spaces
reflexive sheaves
title_short Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
title_full Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
title_fullStr Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
title_full_unstemmed Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
title_sort Classification of the invariants of foliations by curves of low degree on the three-dimensional projective space
dc.creator.none.fl_str_mv Corrêa, M.
Jardim, M.
Marchesi, S.
author Corrêa, M.
author_facet Corrêa, M.
Jardim, M.
Marchesi, S.
author_role author
author2 Jardim, M.
Marchesi, S.
author2_role author
author
dc.subject.none.fl_str_mv Chern classes
Holomorphic foliations by curves
moduli spaces
reflexive sheaves
topic Chern classes
Holomorphic foliations by curves
moduli spaces
reflexive sheaves
description We study foliations by curves on the three-dimensional projective space with no isolated singularities, which is equivalent to assuming that the conormal sheaf is locally free. We provide a classification of the topological and algebraic invariants of the conormal sheaves and singular schemes for such foliations by curves, up to degree 3. In particular, we prove that foliations by curves of degree 1 or 2 are contained in a pencil of planes or are Legendrian, and are given by the complete intersection of two codimension one distributions. Furthermore, we prove that the conormal sheaf of a foliation by curves of degree 3 with reduced singular scheme either splits as a sum of line bundles or is an instanton bundle. For degree larger than 3, we focus on two classes of foliations by curves, namely Legendrian foliations and those whose conormal sheaf is a twisted null-correlation bundle. We give characterizations of such foliations, describe their singular schemes and their moduli spaces. © 2023 Real Sociedad Matemática Española.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/2072/537052
url http://hdl.handle.net/2072/537052
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Revista Matematica Iberoamericana
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 40 p.
application/pdf
dc.publisher.none.fl_str_mv European Mathematical Society Publishing House
publisher.none.fl_str_mv European Mathematical Society Publishing House
dc.source.none.fl_str_mv RECERCAT (Dipòsit de la Recerca de Catalunya)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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