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of A' over k. Since P and A' are centers of v, A' belongs to the set TIPI . Since P' is an isolated point of TIP), we must have dim A'7k = dim P'/k. From this it follows that A' and P' are isomorphic points over k (since P' is a specialization of A' over k) and that consequently the local rings of A' and P' coincide. Since o c o', the local field k(A') contains the local field k(P) of P, and hence A' is an algebraic point over k(P) (since dim A 'lk = dim P'/k = dim P/k). Since TIPi is a variety over k(P), we conclude that TIP) is zero dimensional over k(P) and therefore consists of a finite number of points. This completes the proof. Our "Main Theorem" on birational transformations follows from the above theorem if one takes into account that if V is locally normal at P then (a) V is analytically irreducible at P (Zariski4) and (b) the finite set TIP) necessarily consists of a single point (Zariski3, theorem 8(A) and theorem 10, pp. 512-514).

The Nucleoprotein Content of Whole Nuclei