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Syz transforms for immersed lagrangian multisections

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dc.contributor.authorChan K.-
dc.contributor.authorSuen Y.-H.-
dc.date.available2020-01-31T00:53:36Z-
dc.date.created2019-12-16-
dc.date.issued2019-10-
dc.identifier.issn0002-9947-
dc.identifier.urihttps://pr.ibs.re.kr/handle/8788114/6824-
dc.description.abstract© 2019 American Mathematical SocietyIn this paper, we study the geometry of the SYZ transform on a semiflat Lagrangian torus fibration. Our starting point is an investigation on the relation between Lagrangian surgery of a pair of straight lines in a symplectic 2-torus and the extension of holomorphic vector bundles over the mirror elliptic curve, via the SYZ transform for immersed Lagrangian multisections defined by Arinkin and Joyce [Fukaya category and Fourier transform, AMS/IP Stud. Adv. Math., Amer. Math. Soc., Providence, RI, 2001] and Leung, Yau, and Zaslow [Adv. Theor. Math. Phys. 4 (2000), no. 6, 1319-1341]. This study leads us to a new notion of equivalence between objects in the immersed Fukaya category of a general compact symplectic manifold (M, ω), under which the immersed Floer cohomology is invariant; in particular, this provides an answer to a question of Akaho and Joyce [J. Differential Geom. 86 (2010), no. 3, 831-500, Question 13.15]. Furthermore, if M admits a Lagrangian torus fibration over an integral affine manifold, we prove, under some additional assumptions, that this new equivalence is mirror to an isomorphism between holomorphic vector bundles over the dual torus fibration via the SYZ transform-
dc.description.uri1-
dc.language영어-
dc.publisherAMER MATHEMATICAL SOC-
dc.titleSyz transforms for immersed lagrangian multisections-
dc.typeArticle-
dc.type.rimsART-
dc.identifier.wosid000514301200018-
dc.identifier.scopusid2-s2.0-85075173243-
dc.identifier.rimsid70684-
dc.contributor.affiliatedAuthorSuen Y.-H.-
dc.identifier.doi10.1090/tran/7757-
dc.identifier.bibliographicCitationTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.372, no.8, pp.5747 - 5780-
dc.citation.titleTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY-
dc.citation.volume372-
dc.citation.number8-
dc.citation.startPage5747-
dc.citation.endPage5780-
dc.description.journalClass1-
dc.description.journalRegisteredClassscie-
dc.description.journalRegisteredClassscopus-
dc.subject.keywordPlusHOMOLOGICAL MIRROR SYMMETRY-
dc.subject.keywordPlusFOURIER-TRANSFORM-
dc.subject.keywordPlusTORUS FIBRATIONS-
dc.subject.keywordPlusVECTOR-BUNDLES-
dc.subject.keywordPlusT-DUALITY-
dc.subject.keywordPlusREAL TORI-
dc.subject.keywordPlusMANIFOLDS-
dc.subject.keywordPlusSECTIONS-
dc.subject.keywordPlusSHEAVES-
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Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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