ON MODULI SPACES OF KAHLER-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.