Syntheme
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil, Jean-Pierre Serre and Alexander Grothendieck. Much of the classical terminology, mainly based on case study, was simply abandoned, with the result that books and papers written before this time can be hard to read. This article lists some of this classical terminology, and describes some of the changes in conventions.
Dolgachev (2012) translates many of the classical terms in algebraic geometry into scheme-theoretic terminology. Other books defining some of the classical terminology include Baker (1922a, 1922b, 1923, 1925, 1933a, 1933b), Coolidge (1931), Coxeter (1969), Hudson (1990), Salmon (1879), Semple & Roth (1949).
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