Lagrangian tori in the projective plane
type: Item
instance of: scholarly article
title: Lagrangian tori in the projective plane
zbMATH Open document ID: 1203.53079
author: N. A. Tyurin
published in: Theoretical and Mathematical Physics
publication date: 2009-10-23T00:00:00Z
review text: Among several unknowns in a general study of Lagrangian tori, the Hori-Vafa conjecture was proved under certain assumptions in [\textit{C.-H. Cho, Y.-G. Oh}, Asian J. Math. 10, No.~4, 773--814 (2006; Zbl 1130.53055)]. The author's motivation are also some problems raised by himself in [ArXiv:math/9902027v1 (1999)], in order to relate mirror symmetry and geometric quantization. Related to these problems, the author states a series of five very interesting new conjectures. He proves the first one in the case of \(\mathbb CP^2\): If a smooth Lagrangian fiber is displaceable, then it is not Bohr-Sommerfield with respect to the canonical class, and if this fiber is Bohr-Sommerfield with respect to the canonical class, then it is also monotonic.
reviewed by: Marcela Popescu
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53D12
Mathematics Subject Classification ID: 53D50
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 5620046
zbMATH Keywords: locally Lagrangian torus
zbMATH Keywords: projective plane
zbMATH Keywords: Bohr-Sommerfield condition
MaRDI profile type: Publication
full work available at URL: s11232-009-0001-y
OpenAlex ID: W2044493637
cites work: Homological Algebra of Mirror Symmetry
cites work: Q4434432
cites work: Q3999811
cites work: Geometric quantization and quantum mechanics
cites work: Lagrangian submanifolds and Hamiltonian systems
cites work: Universal maslov class of a Bohr-Sommerfeld Lagrangian embedding into a pseudo-Einstein manifold
cites work: Q5693345
cites work: Notes on monotone Lagrangian twist tori
DOI: 10.1007/S11232-009-0001-Y
description: scientific article; zbMATH DE number 5620046