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Oh, Yong Geun
기하학 수리물리 연구단
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Lagrangian fibers of Gelfand-Cetlin systems

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Title
Lagrangian fibers of Gelfand-Cetlin systems
Author(s)
Yunhyung Cho; Yoosik Kim; Yong-Geun Oh
Publication Date
2020-10
Journal
ADVANCES IN MATHEMATICS, v.372, pp.107304
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Abstract
© 2020 Elsevier Inc. A Gelfand-Cetlin system is a completely integrable system defined on a partial flag manifold whose image is a rational convex polytope called a Gelfand-Cetlin polytope. Motivated by the study of Nishinou-Nohara-Ueda [24] on the Floer theory of Gelfand-Cetlin systems, we provide a detailed description of topology of Gelfand-Cetlin fibers. In particular, we prove that any fiber over an interior point of an r-dimensional face of the Gelfand-Cetlin polytope is an isotropic submanifold and is diffeomorphic to Tr×N for some smooth manifold N and Tr≅(S1)r. We also prove that such N's are exactly the vanishing cycles shrinking to points in the associated toric variety via the toric degeneration. We also devise an algorithm of reading off Lagrangian fibers from the combinatorics of the ladder diagram
URI
https://pr.ibs.re.kr/handle/8788114/7617
DOI
10.1016/j.aim.2020.107304
ISSN
0001-8708
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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