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dc.contributor.authorMiranda Galcerán, Eva
dc.contributor.authorPresas, Francisco
dc.contributor.authorBarbieri Solha, Romero
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2021-05-05T14:36:51Z
dc.date.available2021-05-05T14:36:51Z
dc.date.issued2020
dc.identifier.citationMiranda, E.; Presas, F.; Barbieri Solha, R. Geometric quantization of almost toric manifolds. "Journal of symplectic geometry", 2020, vol. 18, núm. 4, p. 1147-1168.
dc.identifier.issn1527-5256
dc.identifier.otherhttps://arxiv.org/abs/1705.06572
dc.identifier.urihttp://hdl.handle.net/2117/345182
dc.description.abstractKostant gave a model for the geometric quantization via the cohomology associated to the sheaf of flat sections of a pre-quantum line bundle. This model is well-adapted for real polarizations given by integrable systems and toric manifolds. In the latter case, the cohomology can be computed by counting integral points inside the associated Delzant polytope. In this article we extend Kostant’s geometric quantization to semitoric integrable systems and almost toric manifolds. In these cases the dimension of the acting torus is smaller than half of the dimension of the manifold. In particular, we compute the cohomology groups associated to the geometric quantization if the real polarization is the one induced by an integrable system with focus-focus type singularities in dimension four. As an application we determine a model for the geometric quantization of K3 surfaces under this scheme
dc.format.extent22 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject.otherSemitoric
dc.subject.otherFocus-focus
dc.subject.otherGeometric quantization
dc.titleGeometric quantization of almost toric manifolds
dc.typeArticle
dc.contributor.groupUniversitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.identifier.doi10.4310/JSG.2020.v18.n4.a7
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::58 Global analysis, analysis on manifolds
dc.relation.publisherversionhttps://www.intlpress.com/site/pub/pages/journals/items/jsg/content/vols/0018/0004/a007/index.php
dc.rights.accessOpen Access
local.identifier.drac29681085
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/2PE/MTM2015-69135-P
dc.relation.projectidinfo:eu-repo/grantAgreement/AGAUR/RIS3CAT/2017 SGR 932/GEOMVAP
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO/2017/MTM2015-72876-EXP
local.citation.authorMiranda, E.; Presas, F.; Barbieri Solha, R.
local.citation.publicationNameJournal of symplectic geometry
local.citation.volume18
local.citation.number4
local.citation.startingPage1147
local.citation.endingPage1168


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