Email this article Mironov Lagrangian cycles in algebraic varieties
- Authors: Tyurin N.A.1,2
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Affiliations:
- Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics
- International laboratory for Mirror Symmetry and Automorphic Forms, National Research University "Higher School of Economics" (HSE)
- Issue: Vol 212, No 3 (2021)
- Pages: 128-138
- Section: Articles
- URL: https://journals.rcsi.science/0368-8666/article/view/142367
- DOI: https://doi.org/10.4213/sm9407
- ID: 142367
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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.
About the authors
Nikolai Andreevich Tyurin
Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics; International laboratory for Mirror Symmetry and Automorphic Forms, National Research University "Higher School of Economics" (HSE)
Email: ntyurin@theor.jinr.ru
Doctor of physico-mathematical sciences, Professor
References
- А. Е. Миронов, “О новых примерах гамильтоново-минимальных и минимальных лагранжевых подмногообразий в $mathbb{C}^n$ и $mathbb{C}mathrm{P}^n$”, Матем. сб., 195:1 (2004), 89–102
- Н. А. Тюрин, “Псевдоторические структуры: лагранжевы подмногообразия и лагранжевы слоения”, УМН, 72:3(435) (2017), 131–169
- M. Audin, Torus actions on symplectic manifolds, Progr. Math., 93, 2nd rev. ed., Birkhäuser Verlag, Basel, 2004, viii+325 pp.
- Ф. Гриффитс, Дж. Харрис, Принципы алгебраической геометрии, Мир, М., 1982, 864 с.
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