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VOL. 83 | 2019 Symplectic geometry of unbiasedness and critical points of a potential
Alexey Bondal, Ilya Zhdanovskiy

Editor(s) Kentaro Hori, Changzheng Li, Si Li, Kyoji Saito

Abstract

The goal of these notes is to show that the classification problem of algebraically unbiased system of projectors has an interpretation in symplectic geometry. This leads us to a description of the moduli space of algebraically unbiased bases as critical points of a potential function, which is a Laurent polynomial in suitable coordinates. The Newton polytope of the Laurent polynomial is the classical Birkhoff polytope, the set of doubly stochastic matrices. Mirror symmetry interprets the polynomial as a Landau-Ginzburg potential for corresponding Fano variety and relates the symplectic geometry of the variety with systems of unbiased projectors.

Information

Published: 1 January 2019
First available in Project Euclid: 26 December 2019

zbMATH: 07276137

Digital Object Identifier: 10.2969/aspm/08310001

Subjects:

Rights: Copyright © 2019 Mathematical Society of Japan

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