Proposition 1.47 ================ The converse statement is incorrect if the polynomial system is not homogeneous. A counter-example is (Y(X-1), Z(X-1), X): the system is not a regular sequence, but the syzygy module is generated by the syzygies (Z(X-1)*e3-X*e2, Y(X-1)*e3-X*e1, Y(X-1)*e2-Z(X-1)*e1). I thank Vanessa Vitse for sending me this counter-example.