BIRATIONALE TRANSFORMATIONEN (EIN HISTORISCHER ÜBERBLICK)

Abstract

A survey of the historical development of the concept of birational transformations is sketched. The first period from CREMONA till the twenties of the 20th century is based on the classical algebraic methods of the Italian school. The second period operates with ideal-theoretical methods (B. L. VAN DER WAERDEN) and progressed methods of the commutative algebra (product varieties, protections, valuation etc. (O. ZARISKI). In the third period the basic concepts are expressed in the language of schemas.