Ample Divisors and Lagrangian Submanifolds

N. A. Tyurin<sup>ab

a</sup> Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow region, Russia
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: The paper presents a generalization of D. Bykov's construction that realizes a full flag variety as a Lagrangian submanifold in a direct product of projective spaces. The proof of the results relies heavily on standard constructions of algebraic geometry, including the theory of Kähler potentials.

Keywords: algebraic variety, Lagrangian submanifold, Kähler potential.

Received: June 2, 2025
Revised: June 2, 2025
Accepted: June 5, 2025

DOI: 10.4213/tm4470

 English version: Proceedings of the Steklov Institute of Mathematics, 2025, 329, 217–231

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