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Yat-Hin Suen
기하학 수리물리 연구단
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Syz transforms for immersed lagrangian multisections

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Title
Syz transforms for immersed lagrangian multisections
Author(s)
Chan K.; Suen Y.-H.
Publication Date
2019-10
Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v.372, no.8, pp.5747 - 5780
Publisher
AMER MATHEMATICAL SOC
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
URI
https://pr.ibs.re.kr/handle/8788114/6824
ISSN
0002-9947
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > Journal Papers (저널논문)
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2019_YHS_SYZ Transforms for immersed lagrangian multisections.pdfDownload

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