IMMERSED TWO-SPHERES AND SYZ WITH APPLICATION TO GRASSMANNIANS

Hansol Hong; Yoosik Kim; Siu Cheong Lau

doi:10.4310/jdg/1701804149

IMMERSED TWO-SPHERES AND SYZ WITH APPLICATION TO GRASSMANNIANS

Hansol Hong, Yoosik Kim, Siu Cheong Lau

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber in the SYZ program, namely the product of a torus with the immersed two-sphere with a single nodal self-intersection. As an application, we construct immersed Lagrangians in Gr(2,Cⁿ) and OG(1,C⁵) and derive their SYZ mirrors. It recovers the Lie theoretical mirrors constructed by Rietsch. It also gives an effective way to compute stable disks (with non-trivial obstructions) bounded by immersed Lagrangians.

Original language	English
Pages (from-to)	427-507
Number of pages	81
Journal	Journal of Differential Geometry
Volume	125
Issue number	3
DOIs	https://doi.org/10.4310/jdg/1701804149
Publication status	Published - 2023 Nov

Bibliographical note

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© 2023 International Press of Boston, Inc.. All rights reserved.

All Science Journal Classification (ASJC) codes

Analysis
Algebra and Number Theory
Geometry and Topology

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10.4310/jdg/1701804149

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abstract = "We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber in the SYZ program, namely the product of a torus with the immersed two-sphere with a single nodal self-intersection. As an application, we construct immersed Lagrangians in Gr(2,Cn) and OG(1,C5) and derive their SYZ mirrors. It recovers the Lie theoretical mirrors constructed by Rietsch. It also gives an effective way to compute stable disks (with non-trivial obstructions) bounded by immersed Lagrangians.",

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AB - We develop a Floer theoretical gluing technique and apply it to deal with the most generic singular fiber in the SYZ program, namely the product of a torus with the immersed two-sphere with a single nodal self-intersection. As an application, we construct immersed Lagrangians in Gr(2,Cn) and OG(1,C5) and derive their SYZ mirrors. It recovers the Lie theoretical mirrors constructed by Rietsch. It also gives an effective way to compute stable disks (with non-trivial obstructions) bounded by immersed Lagrangians.

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IMMERSED TWO-SPHERES AND SYZ WITH APPLICATION TO GRASSMANNIANS

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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