RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 3, Pages 170–191 (Mi izv8657)  

This article is cited in 1 scientific paper (total in 1 paper)

Special Bohr–Sommerfeld Lagrangian submanifolds of algebraic varieties

N. A. Tyurinab

a Joint Institute for Nuclear Research, Dubna, Moscow region
b National Research University "Higher School of Economics" (HSE), Moscow

Abstract: In this paper we continue our study of special Bohr–Sommerfeld submanifolds in the case when the ambient symplectic manifold possesses a compatible integrable complex structure (and is thus an algebraic variety). In this case we show how to reduce the special Bohr–Sommerfeld geometry to Morse theory on the complements of ample divisors. This gives rise to a construction of Lagrangian shadows of ample divisors in algebraic varieties, which is an example of ‘algebraic v. symplectic’ duality. We suggest a condition for the existence of a Lagrangian shadow and give examples of Lagrangian shadows of ample divisors on the projective plane, complex quadrics and flag manifolds.

Keywords: algebraic variety, Lagrangian submanifold, Bohr–Sommerfeld condition, plurisubharmonic function, gradient flow.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
This paper was written with the support of the Laboratory of Mirror Symmetry in NRU HSE, grant no. 14.641.31.0001 of the government of the Russian Federation.


DOI: https://doi.org/10.4213/im8657

Full text: PDF file (619 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2018, 82:3, 612–631

Bibliographic databases:

UDC: 512.7+514.7+514.8
MSC: 53D12, 53D37
Received: 23.01.2017
Revised: 10.07.2017

Citation: N. A. Tyurin, “Special Bohr–Sommerfeld Lagrangian submanifolds of algebraic varieties”, Izv. RAN. Ser. Mat., 82:3 (2018), 170–191; Izv. Math., 82:3 (2018), 612–631

Citation in format AMSBIB
\Bibitem{Tyu18}
\by N.~A.~Tyurin
\paper Special Bohr--Sommerfeld Lagrangian submanifolds of algebraic varieties
\jour Izv. RAN. Ser. Mat.
\yr 2018
\vol 82
\issue 3
\pages 170--191
\mathnet{http://mi.mathnet.ru/izv8657}
\crossref{https://doi.org/10.4213/im8657}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2018IzMat..82..612T}
\elib{http://elibrary.ru/item.asp?id=34940565}
\transl
\jour Izv. Math.
\yr 2018
\vol 82
\issue 3
\pages 612--631
\crossref{https://doi.org/10.1070/IM8657}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000437922000009}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85049867682}


Linking options:
  • http://mi.mathnet.ru/eng/izv8657
  • https://doi.org/10.4213/im8657
  • http://mi.mathnet.ru/eng/izv/v82/i3/p170

    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, “The moduli space of $D$-exact Lagrangian submanifolds”, Siberian Math. J., 60:4 (2019), 709–719  mathnet  crossref  crossref  isi  elib
  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
    Number of views:
    This page:173
    References:20
    First page:23

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