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• Glossary_of_classical_algebraic_geometry abstract "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, Serre and 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 (1922), Coolidge (1931), Coxeter (1969), Hudson (1990), Salmon (1879), Semple & Roth (1949).".
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• Glossary_of_classical_algebraic_geometry defn Canonical_ring.
• Glossary_of_classical_algebraic_geometry defn "A 1-dimensional family of planes in 3-dimensional projective space .".
• Glossary_of_classical_algebraic_geometry defn "A degree 10 projective variety".
• Glossary_of_classical_algebraic_geometry defn "A regular surface is one whose irregularity is zero.".
• Glossary_of_classical_algebraic_geometry defn "A subvariety of projective space is linearly normal if the linear system defining the embedding is complete; see rational normal curve".
• Glossary_of_classical_algebraic_geometry defn "Degree 10".
• Glossary_of_classical_algebraic_geometry defn "Having no singularities; see regular local ring".
• Glossary_of_classical_algebraic_geometry defn "Local rings are integrally closed; see normal scheme.".
• Glossary_of_classical_algebraic_geometry defn "Orthogonal to the tangent space, such as a line orthogonal to the tangent space or the normal bundle.".
• Glossary_of_classical_algebraic_geometry defn "Related to the complex numbers.".
• Glossary_of_classical_algebraic_geometry defn "The dimension of the space of sections of the canonical bundle, as in the genus of a curve or the geometric genus of a surface".
• Glossary_of_classical_algebraic_geometry defn "The dual curve of a plane curve is the set of its tangent lines, considered as a curve in the dual projective plane.".
• Glossary_of_classical_algebraic_geometry defn "The dual of a projective space is the set of hyperplanes, considered as another projective space".
• Glossary_of_classical_algebraic_geometry defn "The envelope of the normals of a curve".
• Glossary_of_classical_algebraic_geometry defn "The tangent developable of a curve is the surface consisting of its tangent lines.".
• Glossary_of_classical_algebraic_geometry defn "arithmetic genus of a surface".
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• Glossary_of_classical_algebraic_geometry pre "Conventions".
• Glossary_of_classical_algebraic_geometry quote "...we refer to a certain degree of informality of language, sacrificing precision to brevity, ..., and which has long characterized most geometrical writing. ...[The meaning] depends always on the context and is invariably assumed to be capable of unambiguous interpretation by the reader.".
• Glossary_of_classical_algebraic_geometry quote "Most particularly we refer to the recurrent use of such adjectives as `general' or `generic', or such phrases as `in general', whose meaning, wherever they are used, depends always on the context and is invariably assumed to be capable of unambiguous interpretation by the reader.".
• Glossary_of_classical_algebraic_geometry quote "On the other hand, while most of the material treated in the book exists in classical treatises in algebraic geometry, their somewhat archaic terminology and what is by now completely forgotten background knowledge makes these books useful to but a handful of experts in the classical literature.".
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• Glossary_of_classical_algebraic_geometry subject Category:Algebraic_geometry.
• Glossary_of_classical_algebraic_geometry subject Category:Glossaries_of_mathematics.
• Glossary_of_classical_algebraic_geometry subject Category:History_of_geometry.
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• Glossary_of_classical_algebraic_geometry comment "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, Serre and 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.".
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