Secant varieties of toric varieties arising from simplicial complexes

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatori...

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Autores: Khadam, Muhammad Azeem, Michalek, Mateusz, Zwiernik, Piotr
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución: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:10230/46879
Acceso en línea:http://hdl.handle.net/10230/46879
http://dx.doi.org/10.1016/j.laa.2019.12.008
Access Level:acceso abierto
Palabra clave:Secant variety
Segre-Veronese embedding
Simplicial complex
Cumulants
Singular locus
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spelling Secant varieties of toric varieties arising from simplicial complexesKhadam, Muhammad AzeemMichalek, MateuszZwiernik, PiotrSecant varietySegre-Veronese embeddingSimplicial complexCumulantsSingular locusMotivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus.Elsevier202120212020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/10230/46879http://dx.doi.org/10.1016/j.laa.2019.12.008reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésLinear Algebra and its Applications. 2020 Mar 1; 588: 428-457info:eu-repo/grantAgreement/ES/2PE/RYC2017-22544info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00© Elsevier http://dx.doi.org/10.1016/j.laa.2019.12.008info:eu-repo/semantics/openAccessoai:recercat.cat:10230/468792026-05-29T05:05:01Z
dc.title.none.fl_str_mv Secant varieties of toric varieties arising from simplicial complexes
title Secant varieties of toric varieties arising from simplicial complexes
spellingShingle Secant varieties of toric varieties arising from simplicial complexes
Khadam, Muhammad Azeem
Secant variety
Segre-Veronese embedding
Simplicial complex
Cumulants
Singular locus
title_short Secant varieties of toric varieties arising from simplicial complexes
title_full Secant varieties of toric varieties arising from simplicial complexes
title_fullStr Secant varieties of toric varieties arising from simplicial complexes
title_full_unstemmed Secant varieties of toric varieties arising from simplicial complexes
title_sort Secant varieties of toric varieties arising from simplicial complexes
dc.creator.none.fl_str_mv Khadam, Muhammad Azeem
Michalek, Mateusz
Zwiernik, Piotr
author Khadam, Muhammad Azeem
author_facet Khadam, Muhammad Azeem
Michalek, Mateusz
Zwiernik, Piotr
author_role author
author2 Michalek, Mateusz
Zwiernik, Piotr
author2_role author
author
dc.subject.none.fl_str_mv Secant variety
Segre-Veronese embedding
Simplicial complex
Cumulants
Singular locus
topic Secant variety
Segre-Veronese embedding
Simplicial complex
Cumulants
Singular locus
description Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus.
publishDate 2020
dc.date.none.fl_str_mv 2020
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10230/46879
http://dx.doi.org/10.1016/j.laa.2019.12.008
url http://hdl.handle.net/10230/46879
http://dx.doi.org/10.1016/j.laa.2019.12.008
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Linear Algebra and its Applications. 2020 Mar 1; 588: 428-457
info:eu-repo/grantAgreement/ES/2PE/RYC2017-22544
info:eu-repo/grantAgreement/ES/2PE/PGC2018-101643-B-I00
dc.rights.none.fl_str_mv © Elsevier http://dx.doi.org/10.1016/j.laa.2019.12.008
info:eu-repo/semantics/openAccess
rights_invalid_str_mv © Elsevier http://dx.doi.org/10.1016/j.laa.2019.12.008
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv 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
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