RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



TMF:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


TMF, 2010, Volume 162, Number 3, Pages 307–333 (Mi tmf6473)  

This article is cited in 9 scientific papers (total in 9 papers)

Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties

N. A. Tyurinab

a Moscow State University of Railway Engineering (MIIT), Moscow, Russia
b Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: We introduce the notion of a pseudotoric structure on a symplectic manifold, generalizing the notion of a toric structure. We show that such a pseudotoric structure can exist on toric and nontoric symplectic manifolds. For the toric manifolds, it describes deformations of the standard toric Lagrangian fibrations; for the nontoric ones, it gives Lagrangian fibrations with singularities that are very close to the toric fibrations. We present examples of toric manifolds with different pseudotoric structures and prove that certain nontoric manifolds (smooth complex quadrics) have such structures. In the future, introducing this new structure can be useful for generalizing the geometric quantization and mirror symmetry methods that work well in the toric case to a broader class of Fano varieties.

Keywords: toric symplectic manifold, Lagrangian fibration, nondegenerate complex quadric, Bohr–Sommerfeld torus

DOI: https://doi.org/10.4213/tmf6473

Full text: PDF file (493 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 2010, 162:3, 255–275

Bibliographic databases:

Received: 10.04.2009

Citation: N. A. Tyurin, “Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties”, TMF, 162:3 (2010), 307–333; Theoret. and Math. Phys., 162:3 (2010), 255–275

Citation in format AMSBIB
\Bibitem{Tyu10}
\by N.~A.~Tyurin
\paper Pseudotoric Lagrangian fibrations of toric and nontoric Fano varieties
\jour TMF
\yr 2010
\vol 162
\issue 3
\pages 307--333
\mathnet{http://mi.mathnet.ru/tmf6473}
\crossref{https://doi.org/10.4213/tmf6473}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2682127}
\zmath{https://zbmath.org/?q=an:05790854}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2010TMP...162..255T}
\transl
\jour Theoret. and Math. Phys.
\yr 2010
\vol 162
\issue 3
\pages 255--275
\crossref{https://doi.org/10.1007/s11232-010-0021-7}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000276724000001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952070352}


Linking options:
  • http://mi.mathnet.ru/eng/tmf6473
  • https://doi.org/10.4213/tmf6473
  • http://mi.mathnet.ru/eng/tmf/v162/i3/p307

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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, “Chekanov tori and pseudotoric structures”, Russian Math. Surveys, 66:1 (2011), 181–182  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. N. A. Tyurin, “Special Lagrangian fibrations on the flag variety $F^3$”, Theoret. and Math. Phys., 167:2 (2011), 567–576  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    3. S. A. Belev, N. A. Tyurin, “Lifts of Lagrangian Tori”, Math. Notes, 91:5 (2012), 735–737  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. N. A. Tyurin, “Nonstandard Lagrangian tori and pseudotoric structures”, Theoret. and Math. Phys., 171:2 (2012), 700–703  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    5. S. A. Belyov, N. A. Tyurin, “Pseudotoric structures on toric symplectic manifolds”, Theoret. and Math. Phys., 175:2 (2013), 571–579  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. Tyurin N.A., “Exotic Chekanov Tori in Toric Symplectic Varieties”, Xxth International Conference on Integrable Systems and Quantum Symmetries (Isqs-20), Journal of Physics Conference Series, 411, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013, 012028  crossref  isi  scopus
    7. N. A. Tyurin, “Pseudotoric Structures and Lagrangian Spheres in the Flag Variety $F^3$”, Math. Notes, 96:3 (2014), 458–461  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. N. A. Tyurin, “Pseudotoric structures on a hyperplane section of a toric manifold”, Theoret. and Math. Phys., 182:2 (2015), 159–172  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. N. A. Tyurin, “Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations”, Russian Math. Surveys, 72:3 (2017), 513–546  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:378
    Full text:112
    References:56
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020