On moduli spaces of K"ahler-Poisson algebras over rational functions in two variables
K"ahler-Poisson algebras were introduced as algebraic analogues of function algebras on K"ahler manifolds, and it turns out that one can develop geometry for these algebras in a purely algebraic way. A K"ahler-Poisson algebra consists of a Poisson algebra together with the choice of a metric structure, and a natural question arises: For a given Poisson algebra, how many different metric structures are there, such that the resulting K"ahler-Poisson algebras are non-isomorphic? In this paper we initiate a study of such moduli spaces of K"ahler-Poisson algebras defined over rational functions in two variables.
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