the basic statement can be formulated in terms of the picard variety pic("c") of a smooth curve "c", and the subset of pic("c") corresponding to divisor classes of divisors "d", with given values "d" of deg("d") and "r" of "l"("d") − 1 in the notation of the riemann–roch theorem. there is a lower bound ρ for the dimension dim("d", "r", "g") of this subscheme in pic("c"):