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Abelian varieties are a natural generalization of elliptic curves, including algebraic tori in higher dimensions. Just as elliptic curves have a natural moduli space M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} over characteristic 0 constructed as a quotient of the upper-half plane by the action of S L 2 {\displaystyle SL_{2}} , there is an analogous construction for abelian varieties A g {\displaystyle {\mathcal {A}}_{g}} using the Siegel upper half-space and the symplectic group Sp 2 g {\displaystyle \operatorname {Sp} _{2g}}.