# 3-fold

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{{For2|the plants known as "threefold"|Trixis|the chess term|threefold repetition}}

In [algebraic geometry](/source/algebraic_geometry), a '''3-fold''' or '''threefold''' is an [algebraic variety](/source/algebraic_variety) of [dimension](/source/dimension_of_an_algebraic_variety) 3.

The [Mori program](/source/Mori_program) showed that 3-folds have minimal models.

==See also==
* [Algebraic curve](/source/Algebraic_curve)
* [Algebraic surface](/source/Algebraic_surface)
* [Cubic threefold](/source/Cubic_threefold)
* [Quartic threefold](/source/Quartic_threefold)
* [Quintic threefold](/source/Quintic_threefold)

==References==
*{{Citation | last1=Matsuki | first1=Kenji | title=Introduction to the Mori program | publisher=[Springer-Verlag](/source/Springer-Verlag) | location=Berlin, New York | series=Universitext | isbn=978-0-387-98465-0 | mr=1875410 | year=2002}}
*{{Citation | last1=Reid | first1=Miles | author1-link=Miles Reid | title=Journées de Géometrie Algébrique d'Angers, Juillet 1979/Algebraic Geometry, Angers, 1979 | publisher=Sijthoff & Noordhoff | location=Alphen aan den Rijn | mr=605348 | year=1980 | chapter=Canonical 3-folds | pages=273–310}}
*{{Citation | last1=Roth | first1=L. | title=Algebraic threefolds, with special regard to problems of rationality | publisher=[Springer-Verlag](/source/Springer-Verlag) | location=Berlin, New York | series=Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 6 | mr=0076426 | year=1955}}

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Category:3-folds

{{algebraic-geometry-stub}}

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