Symplectic geometry of unbiasedness and critical points of a potential

2015/07/01 by Alexey Bondal, Bondal, Alexey, Ilya Zhdanovskiy +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1507.00081

14 pages

arxiv created 2015/07/01 · arxiv updated 2015/07/02

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 functions, which is a Laurent polynomial in suitable coordinates. The Newton polytope of the Laurent polynomial is the classical Birkhoff polytope, the set of double 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.

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