Irregular hypergeometric D-modules

We study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U...

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Detalles Bibliográficos
Autor: Fernández Fernández, María Cruz
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/42039
Acceso en línea:http://hdl.handle.net/11441/42039
https://doi.org/10.1016/j.aim.2010.01.017
Access Level:acceso abierto
Palabra clave:Hypergeometric D-module
Gevrey series
Slope
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spelling Irregular hypergeometric D-modulesFernández Fernández, María CruzHypergeometric D-moduleGevrey seriesSlopeWe study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U. Walther in [25] still holds for any full rank integer matrix A. We also provide a lower bound for the dimensions of the spaces of Gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters. Holomorphic solutions outside the singular locus of MA(β) can be understood as Gevrey solutions of order one along X at generic points and so they are included as a particular case.Ministerio de Educación y CienciaJunta de AndalucíaEÁlgebraMinisterio de Educación y Ciencia (MEC). EspañaJunta de Andalucía2010info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/42039https://doi.org/10.1016/j.aim.2010.01.017reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésAdvances in Mathematics, 224 (5), 1735-1764.AP2005-2360MTM2007-64509FQM333Amsterdaminfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/420392026-06-17T12:51:07Z
dc.title.none.fl_str_mv Irregular hypergeometric D-modules
title Irregular hypergeometric D-modules
spellingShingle Irregular hypergeometric D-modules
Fernández Fernández, María Cruz
Hypergeometric D-module
Gevrey series
Slope
title_short Irregular hypergeometric D-modules
title_full Irregular hypergeometric D-modules
title_fullStr Irregular hypergeometric D-modules
title_full_unstemmed Irregular hypergeometric D-modules
title_sort Irregular hypergeometric D-modules
dc.creator.none.fl_str_mv Fernández Fernández, María Cruz
author Fernández Fernández, María Cruz
author_facet Fernández Fernández, María Cruz
author_role author
dc.contributor.none.fl_str_mv Álgebra
Ministerio de Educación y Ciencia (MEC). España
Junta de Andalucía
dc.subject.none.fl_str_mv Hypergeometric D-module
Gevrey series
Slope
topic Hypergeometric D-module
Gevrey series
Slope
description We study the irregularity of hypergeometric D-modules MA(β) via the explicit construction of Gevrey series solutions along coordinate subspaces in X = C n. As a consequence, we prove that along coordinate hyperplanes the combinatorial characterization of the slopes of MA(β) given by M. Schulze and U. Walther in [25] still holds for any full rank integer matrix A. We also provide a lower bound for the dimensions of the spaces of Gevrey solutions along coordinate subspaces in terms of volumes of polytopes and prove the equality for very generic parameters. Holomorphic solutions outside the singular locus of MA(β) can be understood as Gevrey solutions of order one along X at generic points and so they are included as a particular case.
publishDate 2010
dc.date.none.fl_str_mv 2010
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/11441/42039
https://doi.org/10.1016/j.aim.2010.01.017
url http://hdl.handle.net/11441/42039
https://doi.org/10.1016/j.aim.2010.01.017
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Advances in Mathematics, 224 (5), 1735-1764.
AP2005-2360
MTM2007-64509
FQM333
Amsterdam
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv E
publisher.none.fl_str_mv E
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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