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The Moduli Space of D-Exact Lagrangian Submanifolds

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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.

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Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Russia

    N. A. Tyurin

  2. Higher School of Economics, Moscow, Russia

    N. A. Tyurin

Authors
  1. N. A. Tyurin
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Correspondence to N. A. Tyurin.

Additional information

Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 4, pp. 907–921.

The author was supported by the Laboratory of Mirror Symmetry of the Higher School of Economics and the Government of the Russian Federation (Grant 14.641.31.0001).

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Tyurin, N.A. The Moduli Space of D-Exact Lagrangian Submanifolds. Sib Math J 60, 709–719 (2019). https://doi.org/10.1134/S0037446619040165

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  • DOI: https://doi.org/10.1134/S0037446619040165

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