Irreducibility of the moduli space of orthogonal instanton bundles on Pn

In order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal i...

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Detalhes bibliográficos
Autores: Andrade, Aline V., Marchesi, Simone, Miró-Roig, Rosa M. (Rosa Maria)
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/193862
Acesso em linha:https://hdl.handle.net/2445/193862
Access Level:acceso abierto
Palavra-chave:Teoria de mòduls
Superfícies algebraiques
Moduli theory
Algebraic surfaces
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spelling Irreducibility of the moduli space of orthogonal instanton bundles on PnAndrade, Aline V.Marchesi, SimoneMiró-Roig, Rosa M. (Rosa Maria)Teoria de mòdulsSuperfícies algebraiquesModuli theoryAlgebraic surfacesIn order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal instanton bundles with no global sections on $\mathbb{P}^n$ and prove that every orthogonal instanton bundle with no global sections on $\mathbb{P}^n$ and charge $c \geq 2$ has rank $r \leq(n-1) c$. We also prove that when the rank $r$ of the bundles reaches the upper bound, $\mathcal{M}_{\mathbb{P}}^{\mathcal{O}}(c, r)$, the coarse moduli space of orthogonal instanton bundles with no global sections on $\mathbb{P}^n$, with charge $c \geq 2$ and rank $r$, is affine, smooth, reduced and irreducible. Last, we construct Kronecker modules to determine the splitting type of the bundles in $\mathcal{M}_{\mathbb{P} n}^{\mathcal{O}}(c, r)$, whenever is non-empty.Springer Nature2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttps://hdl.handle.net/2445/193862Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésVersió postprint del document publicat a: https://doi.org/10.1007/s13163-019-00317-yRevista Matematica Complutense, 2019, vol. 33, p. 271-294https://doi.org/10.1007/s13163-019-00317-y(c) Universidad Complutense de Madrid, 2019info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/1938622026-05-27T06:46:51Z
dc.title.none.fl_str_mv Irreducibility of the moduli space of orthogonal instanton bundles on Pn
title Irreducibility of the moduli space of orthogonal instanton bundles on Pn
spellingShingle Irreducibility of the moduli space of orthogonal instanton bundles on Pn
Andrade, Aline V.
Teoria de mòduls
Superfícies algebraiques
Moduli theory
Algebraic surfaces
title_short Irreducibility of the moduli space of orthogonal instanton bundles on Pn
title_full Irreducibility of the moduli space of orthogonal instanton bundles on Pn
title_fullStr Irreducibility of the moduli space of orthogonal instanton bundles on Pn
title_full_unstemmed Irreducibility of the moduli space of orthogonal instanton bundles on Pn
title_sort Irreducibility of the moduli space of orthogonal instanton bundles on Pn
dc.creator.none.fl_str_mv Andrade, Aline V.
Marchesi, Simone
Miró-Roig, Rosa M. (Rosa Maria)
author Andrade, Aline V.
author_facet Andrade, Aline V.
Marchesi, Simone
Miró-Roig, Rosa M. (Rosa Maria)
author_role author
author2 Marchesi, Simone
Miró-Roig, Rosa M. (Rosa Maria)
author2_role author
author
dc.subject.none.fl_str_mv Teoria de mòduls
Superfícies algebraiques
Moduli theory
Algebraic surfaces
topic Teoria de mòduls
Superfícies algebraiques
Moduli theory
Algebraic surfaces
description In order to obtain existence criteria for orthogonal instanton bundles on $\mathbb{P}^n$, we provide a bijection between equivalence classes of orthogonal instanton bundles with no global sections and symmetric forms. Using such correspondence we are able to provide explicit examples of orthogonal instanton bundles with no global sections on $\mathbb{P}^n$ and prove that every orthogonal instanton bundle with no global sections on $\mathbb{P}^n$ and charge $c \geq 2$ has rank $r \leq(n-1) c$. We also prove that when the rank $r$ of the bundles reaches the upper bound, $\mathcal{M}_{\mathbb{P}}^{\mathcal{O}}(c, r)$, the coarse moduli space of orthogonal instanton bundles with no global sections on $\mathbb{P}^n$, with charge $c \geq 2$ and rank $r$, is affine, smooth, reduced and irreducible. Last, we construct Kronecker modules to determine the splitting type of the bundles in $\mathcal{M}_{\mathbb{P} n}^{\mathcal{O}}(c, r)$, whenever is non-empty.
publishDate 2019
dc.date.none.fl_str_mv 2019
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 https://hdl.handle.net/2445/193862
url https://hdl.handle.net/2445/193862
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1007/s13163-019-00317-y
Revista Matematica Complutense, 2019, vol. 33, p. 271-294
https://doi.org/10.1007/s13163-019-00317-y
dc.rights.none.fl_str_mv (c) Universidad Complutense de Madrid, 2019
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Universidad Complutense de Madrid, 2019
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
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 15,300719

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