Geodesic
Mironov Lagrangian cycles in algebraic varieties
Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 389-398

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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. 
N. A. Tyurin. Mironov Lagrangian cycles in algebraic varieties. Sbornik. Mathematics, Tome 212 (2021) no. 3, pp. 389-398. http://geodesic.mathdoc.fr/item/SM_2021_212_3_a8/
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[2] N. A. Tyurin, “Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations”, Russian Math. Surveys, 72:3 (2017), 513–546 | DOI | DOI | MR | Zbl

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