Jacobian variety
If "G" has genus "g" ≥ 1 then the Σ"n""C" are closely related to the Jacobian variety "J" of "C". More accurately for "n" taking values up to "g" they form a sequence of approximations to "J" from below: their images in "J" under addition on "J" (see theta-divisor) have dimension "n" and fill up "J", with some identifications caused by special divisors.