‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons

In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable &...

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Detalles Bibliográficos
Autores: Antonelli, Vincenzo, Malaspina, Francesco, Marchesi, Simone, Pons Llopis, Joan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2025
País:España
Institución:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/225686
Acceso en línea:https://hdl.handle.net/2445/225686
Access Level:acceso abierto
Palabra clave:Superfícies algebraiques
Homologia
Algebraic surfaces
Homology
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spelling ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantonsAntonelli, VincenzoMalaspina, FrancescoMarchesi, SimonePons Llopis, JoanSuperfícies algebraiquesHomologiaAlgebraic surfacesHomologyIn this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable 't Hooft bundles for each admissible charge $k$. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge $k$. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in $F$ as well as the family of del Pezzo surfaces realized as hyperplane sections of $F$. Finally we investigate the splitting behavior of 't Hooft bundles when restricted to conics.Elsevier Masson2025info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/225686Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1016/j.matpur.2025.103763Journal de Mathématiques Pures et Appliquées, 2025, vol. 202https://doi.org/10.1016/j.matpur.2025.103763cc-by (c) Vincenzo Antonelli et al., 2025http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2256862026-05-27T06:46:51Z
dc.title.none.fl_str_mv ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
title ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
spellingShingle ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
Antonelli, Vincenzo
Superfícies algebraiques
Homologia
Algebraic surfaces
Homology
title_short ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
title_full ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
title_fullStr ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
title_full_unstemmed ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
title_sort ‘t Hooft bundles on the complete flag threefold and moduli spaces of instantons
dc.creator.none.fl_str_mv Antonelli, Vincenzo
Malaspina, Francesco
Marchesi, Simone
Pons Llopis, Joan
author Antonelli, Vincenzo
author_facet Antonelli, Vincenzo
Malaspina, Francesco
Marchesi, Simone
Pons Llopis, Joan
author_role author
author2 Malaspina, Francesco
Marchesi, Simone
Pons Llopis, Joan
author2_role author
author
author
dc.subject.none.fl_str_mv Superfícies algebraiques
Homologia
Algebraic surfaces
Homology
topic Superfícies algebraiques
Homologia
Algebraic surfaces
Homology
description In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$. In particular we prove that there exist $\mu$-stable 't Hooft bundles for each admissible charge $k$. We completely describe the geometric structure of the moduli space of (special) 't Hooft bundles for arbitrary charge $k$. Along the way to reach these goals, we describe the possible structures of multiple curves supported on some rational curves in $F$ as well as the family of del Pezzo surfaces realized as hyperplane sections of $F$. Finally we investigate the splitting behavior of 't Hooft bundles when restricted to conics.
publishDate 2025
dc.date.none.fl_str_mv 2025
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/2445/225686
url https://hdl.handle.net/2445/225686
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/10.1016/j.matpur.2025.103763
Journal de Mathématiques Pures et Appliquées, 2025, vol. 202
https://doi.org/10.1016/j.matpur.2025.103763
dc.rights.none.fl_str_mv cc-by (c) Vincenzo Antonelli et al., 2025
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by (c) Vincenzo Antonelli et al., 2025
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier Masson
publisher.none.fl_str_mv Elsevier Masson
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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score 15,812429

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