Arithmetically Cohen-Macaulay bundles on cubic threefolds

We study arithmetically Cohen-Macaulay bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion sheaves on the projective plane en...

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Autores: Lahoz Vilalta, Martí, Macrì, Emanuele, Stellari, Paolo
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/124871
Acceso en línea:https://hdl.handle.net/2445/124871
Access Level:acceso abierto
Palabra clave:Categories abelianes
Geometria algebraica
Abelian categories
Algebraic geometry
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spelling Arithmetically Cohen-Macaulay bundles on cubic threefoldsLahoz Vilalta, MartíMacrì, EmanueleStellari, PaoloCategories abelianesGeometria algebraicaAbelian categoriesAlgebraic geometryWe study arithmetically Cohen-Macaulay bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion sheaves on the projective plane endowed with the action of a Clifford algebra. We describe this birational isomorphism via wall-crossing in the space of Bridgeland stability conditions, in the example of instanton sheaves of minimal charge.Foundation Compositio Mathematica2015info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/124871Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.14231/AG-2015-011Algebraic Geometry, 2015, vol. 2, num. 2, p. 231-269https://doi.org/10.14231/AG-2015-011cc-by-nc (c) Lahoz Vilalta, Martí et al., 2015http://creativecommons.org/licenses/by-nc/3.0/esinfo:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1248712026-05-27T06:46:51Z
dc.title.none.fl_str_mv Arithmetically Cohen-Macaulay bundles on cubic threefolds
title Arithmetically Cohen-Macaulay bundles on cubic threefolds
spellingShingle Arithmetically Cohen-Macaulay bundles on cubic threefolds
Lahoz Vilalta, Martí
Categories abelianes
Geometria algebraica
Abelian categories
Algebraic geometry
title_short Arithmetically Cohen-Macaulay bundles on cubic threefolds
title_full Arithmetically Cohen-Macaulay bundles on cubic threefolds
title_fullStr Arithmetically Cohen-Macaulay bundles on cubic threefolds
title_full_unstemmed Arithmetically Cohen-Macaulay bundles on cubic threefolds
title_sort Arithmetically Cohen-Macaulay bundles on cubic threefolds
dc.creator.none.fl_str_mv Lahoz Vilalta, Martí
Macrì, Emanuele
Stellari, Paolo
author Lahoz Vilalta, Martí
author_facet Lahoz Vilalta, Martí
Macrì, Emanuele
Stellari, Paolo
author_role author
author2 Macrì, Emanuele
Stellari, Paolo
author2_role author
author
dc.subject.none.fl_str_mv Categories abelianes
Geometria algebraica
Abelian categories
Algebraic geometry
topic Categories abelianes
Geometria algebraica
Abelian categories
Algebraic geometry
description We study arithmetically Cohen-Macaulay bundles on cubic threefolds by using derived category techniques. We prove that the moduli space of stable Ulrich bundles of any rank is always non-empty by showing that it is birational to a moduli space of semistable torsion sheaves on the projective plane endowed with the action of a Clifford algebra. We describe this birational isomorphism via wall-crossing in the space of Bridgeland stability conditions, in the example of instanton sheaves of minimal charge.
publishDate 2015
dc.date.none.fl_str_mv 2015
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 https://hdl.handle.net/2445/124871
url https://hdl.handle.net/2445/124871
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.14231/AG-2015-011
Algebraic Geometry, 2015, vol. 2, num. 2, p. 231-269
https://doi.org/10.14231/AG-2015-011
dc.rights.none.fl_str_mv cc-by-nc (c) Lahoz Vilalta, Martí et al., 2015
http://creativecommons.org/licenses/by-nc/3.0/es
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc (c) Lahoz Vilalta, Martí et al., 2015
http://creativecommons.org/licenses/by-nc/3.0/es
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Foundation Compositio Mathematica
publisher.none.fl_str_mv Foundation Compositio Mathematica
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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