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- 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 translates many of the classical terms in algebraic geometry into scheme-theoretic terminology. Other books defining some of the classical terminology include Baker , , , , , . (en)
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- 82768 (xsd:nonNegativeInteger)
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- dbr:Plurigenus
- A degree 10 projective variety (en)
- Degree 10 (en)
- Having no singularities; see regular local ring. (en)
- The dual curve of a plane curve is the set of its tangent lines, considered as a curve in the dual projective plane. (en)
- A regular surface is one whose irregularity is zero. (en)
- Related to the complex numbers. (en)
- Local rings are integrally closed; see normal scheme. (en)
- The envelope of the normals of a curve (en)
- arithmetic genus of a surface (en)
- A 1-dimensional family of planes in 3-dimensional projective space . (en)
- 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 (en)
- Orthogonal to the tangent space, such as a line orthogonal to the tangent space or the normal bundle. (en)
- A subvariety of projective space is linearly normal if the linear system defining the embedding is complete; see rational normal curve. (en)
- The dual of a projective space is the set of hyperplanes, considered as another projective space. (en)
- The tangent developable of a curve is the surface consisting of its tangent lines. (en)
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- 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. (en)
- ...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. (en)
- 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. (en)
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- 1922 (xsd:integer)
- 1923 (xsd:integer)
- 1925 (xsd:integer)
- 1933 (xsd:integer)
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- 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. (en)
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- Glossary of classical algebraic geometry (en)
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