1. Sur les fonctions algébriques à corps de constantes fini, C.R.t. 210 (1940), p. 592.
2. F. Severi, Trattato di Geometria algebrica,vol. 1, pt. 1, Bologna, Zanichelli 1926, chapter VI. It should be observed that Severi’s treatment, although undoubtedly containing all the essential elements for the solution of the problems it purports to solve, is meant to cover only the classical case where the field of constants is that of complex numbers, and doubts may be raised as to its applicability to more general cases, especially to characteristic p # 0. A rewriting of the whole theory, covering such cases, is therefore a necessary preliminary to the applications we have in view.
3. A generic point of an irreducible variety of dimension n is a point, the coördinates of which satisfy the equations of the variety and generate a field of degree of transcendency n over the field of constants. Cf. B. L. van der Waerden, Einführung in die algebraische Geometrie,Berlin, Springer 1939, chap. IV, §29.
4. B. L. van der Waerden, Zur algebraischen Geometrie XIII, Math. Ann.,115, 359, and XIV, Ibid. 619.
5. Loc. cit.,’ chap. VI, No. 75 (pp. 228–229) and No. 84 (pp. 259–267). Seven’s treatment can be somewhat clarified and simplified at this point, as will be shown elsewhere.