|
This article is cited in 2 scientific papers (total in 2 papers)
The moduli space of $D$-exact Lagrangian submanifolds
N. A. Tyurinab a Joint Institute for Nuclear Research, Dubna, Russia
b Higher School of Economics, Moscow, Russia
Abstract:
This paper studies the Lagrangian geometry of algebraic varieties. Given a smooth compact simply-connected algebraic variety, we construct a family of finite-dimensional Kähler manifolds whose elements are the equivalence classes of Lagrangian submanifolds satisfying our new $D$-exactness condition. In connection with the theory of Weinstein structures, these moduli spaces turn out related to the special Bohr–Sommerfeld geometry constructed by the author previously. This enables us to extract from the moduli spaces some stable components and conjecture that they are not only Kähler but also algebraic.
Keywords:
symplectic manifold, prequantization data, Bohr–Sommerfeld condition, special Bohr–Sommerfeld Lagrangian submanifolds, exact Lagrangian submanifolds, moduli spaces.
Received: 12.10.2018 Revised: 12.10.2018 Accepted: 19.12.2018
Citation:
N. A. Tyurin, “The moduli space of $D$-exact Lagrangian submanifolds”, Sibirsk. Mat. Zh., 60:4 (2019), 907–921; Siberian Math. J., 60:4 (2019), 709–719
Linking options:
https://www.mathnet.ru/eng/smj3124 https://www.mathnet.ru/eng/smj/v60/i4/p907
|
Statistics & downloads: |
Abstract page: | 194 | Full-text PDF : | 119 | References: | 23 | First page: | 5 |
|