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TMF, 2009, Volume 158, Number 1, Pages 3–22 (Mi tmf6296)  

This article is cited in 2 scientific papers (total in 2 papers)

Lagrangian tori in the projective plane

N. A. Tyurinab

a Moscow State University of Railway Communications
b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: We extend the discussion of the homological mirror symmetry for toric manifolds to the more general case of monotonic symplectic manifolds with real polarizations. We claim that the Hori–Vafa conjecture, proved for toric Fano varieties, can be verified in a much wider context. Then the Bohr–Sommerfeld notion regarding the canonical class Lagrangian submanifold appears and plays an important role. A bridge is thus manifested between the geometric quantization and homological mirror symmetry programs for the projective plane in terms of its Lagrangian geometry. This allows using standard facts from the theory of geometric quantization to obtain some results in the framework of the theory of homological mirror symmetry.

Keywords: Lagrangian torus, projective plane, Bohr–Sommerfeld condition

DOI: https://doi.org/10.4213/tmf6296

Full text: PDF file (456 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 158:1, 1–16

Bibliographic databases:

Received: 04.03.2008

Citation: N. A. Tyurin, “Lagrangian tori in the projective plane”, TMF, 158:1 (2009), 3–22; Theoret. and Math. Phys., 158:1 (2009), 1–16

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Tyurin, “Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties”, Theoret. and Math. Phys., 162:3 (2010), 255–275  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. N. A. Tyurin, “Special Bohr–Sommerfeld Lagrangian submanifolds of algebraic varieties”, Izv. Math., 82:3 (2018), 612–631  mathnet  crossref  crossref  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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