GENERALLY RATIONAL POLYNOMIALS IN TWO VARIABLES

Let k be an algebraically closed field. A polynomial F is an element of k[X, Y] is said to be generally rational if, for almost all lambda is an element of k, the curve "F = lambda" is rational. It is well known that, if char k = 0, F is generally rational if there exists G is an element of k(X, Y) such that k(F, G) = k(X, Y). We give analogous results valid in arbitrary characteristic.