Resumen de Integral points on generic fibers
Let P(x, y) be a rational polynomial. If the curve (P(x, y) = k), with k �¸ Q, is irreducible and admits an infinite number of points whose coordinates are integers, then Siegel�fs theorem implies that the curve is rational. We deal with the case where k is a generic value and prove, in the spirit of the Abhyankar.Moh.Suzuki theorem, that there exists an algebraic automorphism sending P(x, y) to the polynomial x or to x2 . y2, with �¸ N. Moreover for such curves we give a sharp bound for the number of integral points (x, y) with x and y bounded.
