Let P(X,Y,Z) denote a homogeneous polynomial in ℂ[X,Y,Z] such that X<sub>P</sub>  =  {(u : v : w) ∈ ℂℙ<sup>2</sup>  |  P(u,v,w) = 0} defines a smooth complex projective curve in ℂℙ<sup>2</sup>. It inherits a Riemannian metric from the Fubini-Study metric on ℂℙ<sup>2</sup>.

Is there an explicit formula or algorithm that gives the area of X<sub>P</sub> as a real surface in terms of the polynomial P(X,Y,Z)?