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Sbornik: Mathematics, 2021, Volume 212, Issue 3, Pages 389–398
DOI: https://doi.org/10.1070/SM9407 (Mi sm9407) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Mironov Lagrangian cycles in algebraic varieties

N. A. Tyurinab

a Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia
b International Laboratory for Mirror Symmetry and Automorphic Forms, National Research University Higher School of Economics, Moscow, Russia
English version PDF (420 kB) Citations (4)
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DOI: https://doi.org/10.1070/SM9407
Abstract: We generalize a construction due to Mironov. Some time ago he presented new examples of minimal and Hamiltonian minimal Lagrangian submanifolds in $\mathbb{C}^n$ and $\mathbb{C} \mathbb{P}^n$. His construction is based on the considerations of a noncomplete toric action of $T^k$, where $k < n$, on subspaces that are invariant with respect to the action of a natural antiholomorphic involution. This situation takes place for a rather broad class of algebraic varieties: complex quadrics, Grassmannians, flag varieties and so on, which makes it possible to construct many new examples of Lagrangian submanifolds in these algebraic varieties.
Bibliography: 4 titles.
Keywords: algebraic variety, symplectic structure, Lagrangian submanifold.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 14.641.31.0001
This research was carried out with the support of the Laboratory for Mirror Symmetry and Automorphic Forms, National Research University Higher School of Economics, RF Government grant, ag. no. 14.641.31.0001.
Received: 12.03.2020 and 25.03.2020
Russian version:
Matematicheskii Sbornik, 2021, Volume 212, Number 3, Pages 128–138
DOI: https://doi.org/10.4213/sm9407
Bibliographic databases:
Document Type: Article
UDC: 514.763.424+514.763.337
MSC: Primary 14M99, 53D12; Secondary 14M15
Language: English
Original paper language: Russian
Citation: N. A. Tyurin, “Mironov Lagrangian cycles in algebraic varieties”, Mat. Sb., 212:3 (2021), 128–138; Sb. Math., 212:3 (2021), 389–398
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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