[math-fun] Polynomial surface of genus g puzzle

Suppose a polynomial P_g(x,y,z) in the x, y, z coordinates of 3-space is such that the locus Z(P_g) := {(x,y,z) in R^3 | P_g(x,y,z) = 0} is topologically the compact surface of genus g. PUZZLE: ------- What is the lowest possible degree D(g) of P_g ??? Give an example. —Dan