Next we shall suppose that C_{1}, C_{2} are embedded nonsingular curves with C_{1} ⊂ P^{2}, C_{2} ⊂ P^{2}, respectively, and that C_{1}, C_{2} has degree d_{1}, d_{2}, respectively, and that d_{1} = d_{2}, and furthermore that C_{1} and C_{2} are isomorphic as abstract nonsingular curves over an algebraically closed field of arbitrary characteristic p, p being either a prime or 0 where here 0 denotes the additive identity of the ring Z of integers which is easily seen to be the Grothendieck group of the additive monoid of natural numbers {0, 1, …}, or which can alternatively be viewed as the divisor class group of projective n-space (here we assume n ≥ 1).