The genus-degree formula for plane curves can be deduced from the adjunction formula. Let "C" ⊂ P2 be a smooth plane curve of degree "d" and genus "g". Let "H" be the class of a hyperplane in P2, that is, the class of a line. The canonical class of P2 is −3"H". Consequently, the adjunction formula says that the restriction of to "C" equals the canonical class of "C". This restriction is the same as the intersection product restricted to "C", and so the degree of the canonical class of "C" is . By the Riemann–Roch theorem, "g" − 1 = ("d"−3)"d" − "g" + 1, which implies the formula