ON THE GENUS OF CURVES OF AN ALGEBRAIC SYSTEM

Professor C. Chevalley has recently pointed out to me the desirability of having a simple algebraic proof of the following theorem: The genus of any curve of an algebraic system of algebraic curves is not greater than the genus of the generic curve of the system. The theorem seems to be well known, but I have sought in vain for a proof of it in the literature(¹). We shall give here a purely algebraic proof of this theorem, based on the idea of the associated form of an algebraic variety, which was introduced by van der Waerden and myself some years ago(²)…