Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






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


Russian Mathematical Surveys, 2017, Volume 72, Issue 3, Pages 513–546
DOI: https://doi.org/10.1070/RM9764
(Mi rm9764)
 

This article is cited in 3 scientific papers (total in 3 papers)

Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations

N. A. Tyurinabc

a Joint Institute of Nuclear Research, Bogolyubov Theoretical Physics Laboratory
b National Research University "Higher School of Economics", Laboratory of Algebraic Geometry and Applications
c Moscow State University of Transport
References:
Abstract: This survey presents a generalization of the notion of a toric structure on a compact symplectic manifold: the notion of a pseudotoric structure. The language of these new structures appears to be a convenient and natural tool for describing many non-standard Lagrangian submanifolds and cycles (Chekanov's exotic tori, Mironov's cycles in certain particular cases, and others) as well as for constructing Lagrangian fibrations (for example, special fibrations in the sense of Auroux on Fano varieties). Known properties of pseudotoric structures and constructions based on these properties are discussed, as well as open problems whose solution may be of importance in symplectic geometry and mathematical physics.
Bibliography: 28 titles.
Keywords: symplectic manifold, Lagrangian submanifold, Lagrangian fibration, toric manifold, Delzant polytope, exotic Lagrangian tori.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 5-100
This paper was written with the support of the programme “Increasing the Competitiveness of Leading Universities of the Russian Federation” (project no. 5-100).
Received: 30.01.2017
Revised: 21.02.2017
Bibliographic databases:
Document Type: Article
UDC: 516.5
MSC: Primary 53D05, 53D12; Secondary 14M15, 14M25, 53D50
Language: English
Original paper language: Russian
Citation: N. A. Tyurin, “Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations”, Russian Math. Surveys, 72:3 (2017), 513–546
Citation in format AMSBIB
\Bibitem{Tyu17}
\by N.~A.~Tyurin
\paper Pseudotoric structures: Lagrangian~submanifolds and Lagrangian fibrations
\jour Russian Math. Surveys
\yr 2017
\vol 72
\issue 3
\pages 513--546
\mathnet{http://mi.mathnet.ru//eng/rm9764}
\crossref{https://doi.org/10.1070/RM9764}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3662461}
\zmath{https://zbmath.org/?q=an:1386.53095}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2017RuMaS..72..513T}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000412068800004}
\elib{https://elibrary.ru/item.asp?id=29833702}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85030652295}
Linking options:
  • https://www.mathnet.ru/eng/rm9764
  • https://doi.org/10.1070/RM9764
  • https://www.mathnet.ru/eng/rm/v72/i3/p131
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024