I'm reading my Algebraic geometry textbook and wanted to know if they interchange the words varieties and affine varieties. Just beginning my studies and didn't want to make any assumptions.
Is there a difference between varieties and affine varieties, if so what is it?
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algebraic-geometry
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6Which book? It depends very much on local conventions. But any serious book on the subject will want to talk about projective varieties, which are not affine outside of trivial cases. More generally one will want objects that look locally like affine varieties, but this usually waits until schemes have been introduced. – 2012-07-23
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4Usually a variety is defined as something *locally* an affine variety. For example, projective space is a variety, but it is not an affine variety. (but the answer to this question really depends upon the convenctions of your textboox) – 2012-07-23