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dc.contributor.authorHicks, Jeffrey
dc.date.accessioned2021-03-26T16:20:56Z
dc.date.available2021-03-26T16:20:56Z
dc.date.issued2021-01-06
dc.identifier.issn1022-1824
dc.identifier.others00029-020-00614-1
dc.identifier.other614
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/319243
dc.descriptionFunder: University of Cambridge
dc.description.abstractAbstract: We look at how one can construct from the data of a dimer model a Lagrangian submanifold in (C∗)n whose valuation projection approximates a tropical hypersurface. Each face of the dimer corresponds to a Lagrangian disk with boundary on our tropical Lagrangian submanifold, forming a Lagrangian mutation seed. Using this we find tropical Lagrangian tori LT2 in the complement of a smooth anticanonical divisor of a toric del-Pezzo whose wall-crossing transformations match those of monotone SYZ fibers. An example is worked out for the mirror pair (CP2\E, W), Xˇ9111. We find a symplectomorphism of CP2\E interchanging LT2 and a SYZ fiber. Evidence is provided that this symplectomorphism is mirror to fiberwise Fourier–Mukai transform on Xˇ9111.
dc.languageen
dc.publisherSpringer International Publishing
dc.subjectArticle
dc.subject53D37
dc.subject14T05
dc.titleTropical Lagrangians in toric del-Pezzo surfaces
dc.typeArticle
dc.date.updated2021-03-26T16:20:55Z
prism.issueIdentifier1
prism.publicationNameSelecta Mathematica
prism.volume27
dc.identifier.doi10.17863/CAM.66363
dcterms.dateAccepted2020-11-29
rioxxterms.versionofrecord10.1007/s00029-020-00614-1
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.identifier.eissn1420-9020


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